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1
Zhu, Rongchan [Verfasser]. "SDE and BSDE on Hilbert spaces: applications to quasi-linear evolution equations and the asymptotic properties of the stochastic quasi-geostrophic equation / Rongchan Zhu. Fakultät für Mathematik." Bielefeld : Universitätsbibliothek Bielefeld, Hochschulschriften, 2012. http://d-nb.info/1021059471/34.
2
Rakesh, Arora. "Fine properties of solutions for quasi-linear elliptic and parabolic equations with non-local and non-standard growth." Thesis, Pau, 2020. http://www.theses.fr/2020PAUU3021.
Анотація:
Dans cette thèse, nous étudions les propriétés fines des solutions d'équations elliptiques et paraboliques quasi-linéaires impliquant une croissance non locale et non standard. Nous nous sommes concentrés sur trois différents types d’équations aux dérivées partielles (EDP).Dans un premier temps, nous étudions les propriétés qualitatives des solutions faibles et fortes d’équations d'évolution comportant des termes à croissance non-standard. La motivation de l'étude de ces types d'équations réside dans la modélisation de caractéristiques anisotropes se produisant dans les modèles de fluides électro-rhéologiques, la restauration d'images, le processus de filtration dans les milieux complexes, les problèmes de stratigraphie ou encore les interactions biologiques hétérogènes. Dans cette étude, nous déterminons des conditions suffisantes sur les données initiales pour obtenir l'existence et l'unicité de solution forte. Nous établissons également la régularité de second ordre de la solution forte ainsi que des résultats optimaux d'intégrabilité à l’aide de nouvelles inégalités d'interpolation.Nous étudions en outre les propriétés des solutions faibles de problèmes doublement non-linéaires impliquant premièrement une classe d'opérateurs de type Leray-Lions et une non-linéarité dans la dérivée temporelle. Nous considérons les questions d'existence, d'unicité, de régularité ainsi que de comportement à l’infini des solutions faibles de ces problèmesDans une deuxième étude, nous considérons des systèmes de type Kirchhoff impliquant des opérateurs non-linéaires de type Choquard avec des poids singuliers. Cette classe de problèmes apparaît dans de nombreux phénomènes physiques comme la variation de longueur d’une corde tendue en vibration où le terme de Kirchhoff mesure le changement de tension ou encore la propagation d’ondes électromagnétiques dans le plasma. Motivé par les nombreuses applications physiques, nous étudions cette classe d’équations et nous établissons l'existence et des résultats de non-unicité pour des systèmes impliquant le n-Laplacien et des opérateurs polyharmoniques à l’aide d’inégalités de type Adams, Moser et Trudinger.Enfin, nous étudions des problèmes singuliers impliquant des opérateurs non-locaux comme le p-Laplacien fractionnaire. Nous établissons l'existence et la multiplicité des solutions classiques dans le cas du Laplacien fractionnaire impliquant une non-linéarité exponentielle en utilisant la théorie des bifurcations. Pour caractériser le comportement des grandes solutions, nous étudions en détail les singularités isolées pour l'équation elliptique semi-linéaire singulière. Nous obtenons la symétrie de la solution classique du problème Laplacien fractionnaire grâce à la méthode du plan mobile et d’un principe du maximum. Nous étudions également le problème de p-Laplacian fractionnaire non-linéaire impliquant une non-linéarité singulière et des poids singuliers. Nous montrons l'existence/ non-existence, l'unicité et la régularité holdérienne en exploitant le comportement des solutions proche du bord du domaine et par des méthodes d'approximationIn this thesis, we study the fine properties of solutions to quasilinear elliptic and parabolic equations involving non-local and non-standard growth. We focus on three different types of partial differential equations (PDEs).Firstly, we study the qualitative properties of weak and strong solutions of the evolution equations with non-standard growth. The importance of investigating these kinds of evolutions equations lies in modeling various anisotropic features that occur in electrorheological fluids models, image restoration, filtration process in complex media, stratigraphy problems, and heterogeneous biological interactions. We derive sufficient conditions on the initial data for the existence and uniqueness of a strong solution of the evolution equation with Dirichlet type boundary conditions. We establish the global higher integrability and second-order regularity of the strong solution via proving new interpolation inequalities. We also study the existence, uniqueness, regularity, and stabilization of the weak solution of Doubly nonlinear equation driven by a class of Leray-Lions type operators and non-monotone sub-homogeneous forcing terms. Secondly, we study the Kirchhoff equation and system involving different kinds of non-linear operators with exponential nonlinearity of the Choquard type and singular weights. These type of problems appears in many real-world phenomena starting from the study in the length of the string during the vibration of the stretched string, in the study of the propagation of electromagnetic waves in plasma, Bose-Einstein condensation and many more. Motivating from the abundant physical applications, we prove the existence and multiplicity results for the Kirchhoff equation and system with subcritical and critical exponential non-linearity, that arise out of several inequalities proved by Adams, Moser, and Trudinger. To deal with the system of Kirchhoff equations, we prove new Adams, Moser and Trudinger type inequalities in the Cartesian product of Sobolev spaces.Thirdly, we study the singular problems involving nonlocal operators. We show the existence and multiplicity for the classical solutions of Half Laplacian singular problem involving exponential nonlinearity via bifurcation theory. To characterize the behavior of large solutions, we further study isolated singularities for the singular semi linear elliptic equation. We show the symmetry and monotonicity properties of classical solution of fractional Laplacian problem using moving plane method and narrow maximum principle. We also study the nonlinear fractional Laplacian problem involving singular nonlinearity and singular weights. We prove the existence, uniqueness, non-existence, optimal Sobolev and Holder regularity results via exploiting the C^1,1 regularity of the boundary, barrier arguments and approximation method
3
Mokrane, Abdelhafid. "Existence de solutions pour certains problèmes quasi linéaires elliptiques et paraboliques." Paris 6, 1986. http://www.theses.fr/1986PA066086.
Анотація:
Existence de solutions bornées pour certaines équations paraboliques non linéaires. Existence de solutions pour un système elliptique quasi linéaire à croissance quadratique grâce à une borne l’infini petite. Existence de solutions pour un système elliptique quasi linéaire avec un second membre à croissance quadratique ayant une structure particulière.
4
Maach, Fatna. "Existence pour des systèmes de réaction-diffusion ou quasi linéaires avec loi de balance." Nancy 1, 1994. http://www.theses.fr/1994NAN10121.
Анотація:
Notre étude concerne des problèmes d'existence (ou de non-existence) pour des systèmes de réaction-diffusion elliptiques quasi linéaires présentant deux propriétés essentielles et fréquentes dans les applications, à savoir: 1) les solutions (éventuelles) sont positives; 2) la masse totale des composants est a priori contrôlée: ceci correspond à une propriété structurelle des termes non linéaires, par exemple que leur somme est négative ou nulle. Pour les systèmes semi-linéaires deux fois deux, c'est-à-dire lorsque les termes non linéaires sont indépendants des gradients et dans le cas ou l'un des composants est de plus a priori contrôlé, nous faisons une étude complète. Nous analysons en particulier l'influence des données au bord relativement à l'existence ou la non-existence des solutions. Nous montrons ainsi, moyennant certaines hypothèses, que pour la plupart des combinaisons de données au bord, on a existence. Des résultats négatifs sont donnés pour les autres types de données au bord. Quand les termes non linéaires dépendent des gradients et quand cette dépendance est sous-quadratique, nous obtenons l'existence de solutions classiques. Nous donnons également un résultat d'existence lorsque les données sont très peu régulières. Nous étudions enfin le cas de croissance quadratique ou sur-quadratique et nous montrons l'existence de solutions classiques si les operateurs de diffusions sont proportionnels
5
Jonsson, Karl. "Two Problems in non-linear PDE’s with Phase Transitions." Licentiate thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223562.
Анотація:
This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. The time evolution of the space that the fluid occupies can be modelled by a semi-linear PDE. This is a problem within the field of free boundary problems. In the multi-phase problem we consider the time-evolution of a system of phases which interact according to the principle that the joint boundary which emerges when two phases meet is fixed for all future times. The problem is handled by introducing a parameterized equation which is regularized and penalized. The penalization is non-local in time and tracks the history of the system, penalizing the joint support of two different phases in space-time. The main result in the first paper is the existence theory of a weak solution to the parameterized equations in a Bochner space using the implicit function theorem. The family of solutions to the parameterized problem is uniformly bounded allowing us to extract a weakly convergent subsequence for the case when the penalization tends to infinity. The second problem deals with a parameterized highly oscillatory quasi-linear elliptic equation in divergence form. As the regularization parameter tends to zero the equation gets a jump in the conductivity which occur at the level set of a locally periodic function, the obstacle. As the oscillations in the problem data increases the solution to the equation experiences high frequency jumps in the conductivity, resulting in the corresponding solutions showing an effective global behaviour. The global behavior is related to the so called homogenized solution. We show that the parameterized equation has a weak solution in a Sobolev space and derive bounds on the solutions used in the analysis for the case when the regularization is lost. Surprisingly, the limiting problem in this case includes an extra term describing the interaction between the solution and the obstacle, not appearing in the case when obstacle is the zero level-set. The oscillatory nature of the problem makes standard numerical algorithms computationally expensive, since the global domain needs to be resolved on the micro scale. We develop a multi scale method for this problem based on the heterogeneous multiscale method (HMM) framework and using a finite element (FE) approach to capture the macroscopic variations of the solutions at a significantly lower cost. We numerically investigate the effect of the obstacle on the homogenized solution, finding empirical proof that certain choices of obstacles make the limiting problem have a form structurally different from that of the parameterized problem.QC 20180222
6
Drogoul, Audric. "Méthode du gradient topologique pour la détection de contours et de structures fines en imagerie." Thesis, Nice, 2014. http://www.theses.fr/2014NICE4063/document.
Анотація:
Cette thèse porte sur la méthode du gradient topologique appliquée au traitement d'images. Principalement, on s'intéresse à la détection d'objets assimilés, soit à des contours si l'intensité de l'image à travers la structure comporte un saut, soit à une structure fine (filaments et points en 2D) s'il n'y a pas de saut à travers la structure. On commence par généraliser la méthode du gradient topologique déjà utilisée en détection de contours pour des images dégradées par du bruit gaussien, à des modèles non linéaires adaptés à des images contaminées par un processus poissonnien ou du bruit de speckle et par différents types de flous. On présente également un modèle de restauration par diffusion anisotrope utilisant le gradient topologique pour un domaine fissuré. Un autre modèle basé sur une EDP elliptique linéaire utilisant un opérateur anisotrope préservant les contours est proposé. Ensuite, on présente et étudie un modèle de détection de structures fines utilisant la méthode du gradient topologique. Ce modèle repose sur l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées secondes d'une régularisation de l'image solution d'une EDP d'ordre 4 de type Kirchhoff. En particulier on explicite les gradients topologiques pour des domaines 2D fissurés ou perforés, et des domaines 3D fissurés. Plusieurs applications pour des images 2D et 3D, floutées et contaminées par du bruit gaussien, montrent la robustesse et la rapidité de la méthode. Enfin on généralise notre approche pour la détection de contours et de structures fines par l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées m−ième d'une régularisation de l'image dégradée, solution d'une EDP d'ordre 2mThis thesis deals with the topological gradient method applied in imaging. Particularly, we are interested in object detection. Objects can be assimilated either to edges if the intensity across the structure has a jump, or to fine structures (filaments and points in 2D) if there is no jump of intensity across the structure. We generalize the topological gradient method already used in edge detection for images contaminated by Gaussian noise, to quasi-linear models adapted to Poissonian or speckled images possibly blurred. As a by-product, a restoration model based on an anisotropic diffusion using the topological gradient is presented. We also present a model based on an elliptical linear PDE using an anisotropic differential operator preserving edges. After that, we study a variational model based on the topological gradient to detect fine structures. It consists in the study of the topological sensitivity of a cost function involving second order derivatives of a regularized version of the image solution of a PDE of Kirchhoff type. We compute the topological gradients associated to perforated and cracked 2D domains and to cracked 3D domains. Many applications performed on 2D and 3D blurred and Gaussian noisy images, show the robustness and the fastness of the method. An anisotropic restoration model preserving filaments in 2D is also given. Finally, we generalize our approach by the study of the topological sensitivity of a cost function involving the m − th derivatives of a regularization of the image solution of a 2m order PDE
7
Qi, Yuan-Wei. "The blow-up of quasi-linear parabolic equations." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253381.
8
Furlan, Marco. "Structures contrôlées pour les équations aux dérivées partielles." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED008/document.
Анотація:
Le projet de thèse comporte différentes directions possibles: a) Améliorer la compréhension des relations entre la théorie des structures de régularité développée par M. Hairer et la méthode des Distributions Paracontrolées développée par Gubinelli, Imkeller et Perkowski, et éventuellement fournir une synthèse des deux. C'est très spéculatif et, pour le moment, il n'y a pas de chemin clair vers cet objectif à long terme. b) Utiliser la théorie des Distributions Paracontrolées pour étudier différents types d'équations aux dérivés partiels: équations de transport et équations générales d'évolution hyperbolique, équations dispersives, systèmes de lois de conservation. Ces EDP ne sont pas dans le domaine des méthodes actuelles qui ont été développées principalement pour gérer les équations d'évolution semi-linéaire parabolique. c) Une fois qu'une théorie pour l'équation de transport perturbée par un signal irregulier a été établie, il sera possible de se dédier à l'étude des phénomènes de régularisation par le bruit qui, pour le moment, n'ont étés étudiés que dans le contexte des équations de transport perturbées par le mouvement brownien, en utilisant des outils standard d'analyse stochastique. d) Les techniques du Groupe de Renormalisation (GR) et les développements multi-échelles ont déjà été utilisés à la fois pour aborder les EDP et pour définir des champs quantiques euclidiens. La théorie des Distributions Paracontrolées peut être comprise comme une sorte d'analyse multi-échelle des fonctionnels non linéaires et il serait intéressant d'explorer l'interaction des techniques paradifférentielles avec des techniques plus standard, comme les "cluster expansions" et les méthodes liées au GRThe thesis project has various possible directions: a) Improve the understanding of the relations between the theory of Regularity Structures developed by M.Hairer and the method of Paracontrolled Distributions developed by Gubinelli, Imkeller and Perkowski, and eventually to provide a synthesis. This is highly speculative and at the moment there are no clear path towards this long term goal. b) Use the theory of Paracontrolled Distributions to study different types of PDEs: transport equations and general hyperbolic evolution equation, dispersive equations, systems of conservation laws. These PDEs are not in the domain of the current methods which were developed mainly to handle parabolic semilinear evolution equations. c) Once a theory of transport equation driven by rough signals have been established it will become possible to tackle the phenomena of regularization by transport noise which for the moment has been studied only in the context of transport equations driven by Brownian motion, using standard tools of stochastic analysis. d) Renormalization group (RG) techniques and multi-scale expansions have already been used both to tackle PDE problems and to define Euclidean Quantum Field Theories. Paracontrolled Distributions theory can be understood as a kind of mul- tiscale analysis of non-linear functionals and it would be interesting to explore the interplay of paradifferential techniques with more standard techniques like cluster expansions and RG methods
9
Samarawickrama-Kuruppuge, Paduma E. "On the Reducibility of Systems of Quasi-Periodic Linear Functional Differential Equations." University of Toledo / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1556815414015887.
10
Moraes, Elisandra de Fátima Gloss de. "Existencia e concentração de soluções para equações de Schrodinger quase-lineares." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307292.
Анотація:
Orientadores: João Marcos Bezerra do O, Djairo Guedes de FigueiredoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho, estudamos questões relacionadas com existência e concentração de soluções positivas para algumas classes de problemas elípticos quase-lineares. Na obtenção de nossos resultados usamos um método variacional que permite estudar soluções do tipo "singlepeak" e "multiple-peak" para uma classe bem geral de não linearidades que não satisfazem necessariamente a condição clássica de Ambrosetti-Rabinowitz bem como nenhuma hipótese de monotonicidade. Problemas deste tipo aparecem em vários modelos da física e biologia, onde a presença de pequenos parâmetros de difusão ocorre naturalmente. Na Física de Plasmas, por exemplo, surgem no estudo de ondas estacionárias para certas classes de problemas envolvendo equações de Schrödinger quase-lineares
Abstract: In this work we study questions related with existence and concentration of positive solutions for some classes of quasilinear elliptic problems. To obtain our results we use a variational method that allows us to study solutions of the "single-peak" and "multiple-peak" type for a more general class of nonlinearities which do not satisfy necessarily the Ambrosetti-Rabinowitz condition and monotonicity hypothesis. Problems of this type appear in several models of physics and biology where the presence of small parameters of difusion occurs naturally. In plasma physics for example, they arise in the study of stationary waves for certain classes of quasilinear Schrödinger equations
Doutorado
Analise
Doutor em Matemática
11
Silva, Kênio Alexsom de Almeida 1979. "Auto-adjunticidade não-linear e leis de conservação para equações evolutivas sobre superfícies regulares." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306724.
Анотація:
Orientador: Yuri Dimitrov BozhkovTese (doutorado) ¿ Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Nesta tese estudamos o conceito novo de equações diferenciais não - linearmente auto-adjuntas para duas classes gerais de equações evolutivas de segunda ordem quase lineares. Uma vez que essas equações não provêm de um problema variacional, não podemos obter leis de conservação via o Teorema de Noether. Por isto aplicamos tal conceito e o Novo Teorema sobre Leis de Conservação de Nail H. Ibragimov, o qual possibilita-nos a determinação de leis de conservação para qualquer equação diferencial. Obtivemos em ambas as classes, equações não - linearmente auto-adjuntos e leis de conservação para alguns casos particularmente importantes: a) as equações do fluxo de Ricci geométrico, do fluxo de Ricci 2D, do fluxo de Ricci modificada e a equação do calor não-linear, na primeira classe; b) as equações do fluxo geométrico hiperbólico e do fluxo geométrica hiperbólica modificada, na segunda classe de equações evolutivas
Abstract: In this thesis we study the new concept of nonlinear self-adjoint deferential equations for two general classes of quasilinear 2D second order evolution equations. Since these equations do not come from a variational problem, we cannot obtain conservation laws via the Noether's Theorem. Therefore we apply this concept and the New Conservation Theorem of Nail H. Ibragimov, which enables one to establish the conservation laws for any deferential equation. We obtain in classes, nonlinear self-adjoint equations and conservation laws for important particular cases: a) the Ricci flow geometric equation, Ricci flow 2D equation, the modified Ricci flow equation and the nonlinear heat equation in the first class; b) the hyperbolic geometric flow equation and the modified hyperbolic geometric flow equation in the second class of evolution equations
Doutorado
Matematica Aplicada
Doutor em Matemática Aplicada
12
Ali, Zakaria Idriss. "Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth." Diss., University of Pretoria, 2010. http://hdl.handle.net/2263/29519.
Анотація:
In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an existence result for such type of stochastic differential equations with non-standard growth conditions. The main difficulty in the present problem is that the existence cannot be easily retrieved from the well known results under Lipschitz type of growth conditions [42].Dissertation (MSc)--University of Pretoria, 2010.
Mathematics and Applied Mathematics
unrestricted
13
Steinbrecher, Andreas. "Numerical solution of quasi-linear differential-Algebraic equations and industrial simulation of multibody systems." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980015936.
14
Ernst, Oliver G. "Minimal and orthogonal residual methods and their generalizations for solving linear operator equations." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-3293998.
Анотація:
This thesis is concerned with the solution of linear operator equations by projection methods known as minimal residual (MR) and orthogonal residual (OR) methods. We begin with a rather abstract framework of approximation by orthogonal and oblique projection in Hilbert space. When these approximation schemes are applied to sequences of nested spaces, with a simple requirement relating trial and test spaces in case of the OR method, one can derive at this rather general level the basic relations which have been proved for many specific Krylov subspace methods for solving linear systems of equations in the literature. The crucial quantities with which we describe the behavior of these methods are angles between subspaces. By replacing the given inner product with one that is basis-dependent, one can also incorporate methods based on non-orthogonal bases such as those based on the non-Hermitian Lanczos process for solving linear systems. In fact, one can show that any reasonable approximation method based on a nested sequence of approximation spaces can be interpreted as an MR or OR method in this way. When these abstract approximation techniques are applied to the solution of linear operator equations, there are three generic algorithmic formulations, which we identify with some algorithms in the literature. Specializing further to Krylov trial and test spaces, we recover the well known Krylov subspace methods. Moreover, we show that our general framework also covers in a natural way many recent generalizations of Krylov subspace methods, which employ techniques such as augmentation, deflation, restarts and truncation. We conclude with a chapter on error and residual bounds, deriving some old and new results based on the angles framework. This work provides a natural and consistent framework for the sometimes confusing plethora of methods of Krylov subspace type introduced in the last 50 years.
15
Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.
Анотація:
This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an important equation to such fields as signal processing, communications, and information theory where singularities propagate throughout space as a function of time. Chapter 3 discusses some concepts and implications of elliptic SPDE's driven by additive noise. These systems are key for understanding steady state phenomena. Chapter 4 presents some numerical work regarding elliptic SPDE's driven by multiplicative and general noise. These SPDE's are open topics in the theoretical literature, hence numerical work provides significant insight into the nature of the process. Chapter 5 presents some numerical work regarding quasi-geostrophic geophysical fluid dynamics involving stochastic noise and demonstrates how these systems can be represented as a combination of elliptic and hyperbolic components.
16
Ernst, Oliver G. "Minimal and orthogonal residual methods and their generalizations for solving linear operator equations." Doctoral thesis, [S.l. : s.n.], 2000. https://tubaf.qucosa.de/id/qucosa%3A22355.
Анотація:
This thesis is concerned with the solution of linear operator equations by projection methods known as minimal residual (MR) and orthogonal residual (OR) methods. We begin with a rather abstract framework of approximation by orthogonal and oblique projection in Hilbert space. When these approximation schemes are applied to sequences of nested spaces, with a simple requirement relating trial and test spaces in case of the OR method, one can derive at this rather general level the basic relations which have been proved for many specific Krylov subspace methods for solving linear systems of equations in the literature. The crucial quantities with which we describe the behavior of these methods are angles between subspaces. By replacing the given inner product with one that is basis-dependent, one can also incorporate methods based on non-orthogonal bases such as those based on the non-Hermitian Lanczos process for solving linear systems. In fact, one can show that any reasonable approximation method based on a nested sequence of approximation spaces can be interpreted as an MR or OR method in this way. When these abstract approximation techniques are applied to the solution of linear operator equations, there are three generic algorithmic formulations, which we identify with some algorithms in the literature. Specializing further to Krylov trial and test spaces, we recover the well known Krylov subspace methods. Moreover, we show that our general framework also covers in a natural way many recent generalizations of Krylov subspace methods, which employ techniques such as augmentation, deflation, restarts and truncation. We conclude with a chapter on error and residual bounds, deriving some old and new results based on the angles framework. This work provides a natural and consistent framework for the sometimes confusing plethora of methods of Krylov subspace type introduced in the last 50 years.
17
Rodrigues, Letícia Faleiros Chaves [UNESP]. "Estabilidade de equações de diferenças quase lineares." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/94368.
Анотація:
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rodrigues_lfc_me_rcla.pdf: 3294088 bytes, checksum: 57f854a99e6fafae6c0f6e3d89de4122 (MD5)O objetivo principal deste trabalho é estudar a estabilidade de equações de diferen- ças do tipo quase lineares utilizando o Método de Linearização, visando sua aplicação na análise de modelos na área de Biologia e Economia
The main objective of this work is to study the stability of almost linear di erence equations, by using the Linearization Method, in order to use in the analysis of some models in Biology and Economy
18
Rodrigues, Letícia Faleiros Chaves. "Estabilidade de equações de diferenças quase lineares /." Rio Claro, 2013. http://hdl.handle.net/11449/94368.
Анотація:
Orientador: Suzinei Aparecida Siqueira MarconatoBanca: Renata Zotin Fomes de Oliveira
Banca: Antônio Carlos da Silva Filho
Resumo: O objetivo principal deste trabalho é estudar a estabilidade de equações de diferenças do tipo quase lineares utilizando o Método de Linearização, visando sua aplicação na análise de modelos na área de Biologia e Economia
Abstract: The main objective of this work is to study the stability of almost linear di erence equations, by using the Linearization Method, in order to use in the analysis of some models in Biology and Economy
Mestre
19
Taha, Abdel-Kaddous. "Solutions periodiques et quasi-periodiques d'une equation de duffing non autonome a double excitation periodique." Toulouse, INSA, 1987. http://www.theses.fr/1987ISAT0002.
Анотація:
On considere un systeme dynamique non lineaire de type duffing, avec une composante periodique parametrique dans la force de rappel et une force exterieure periodique de pulsation differente de celle de la force parametrique
20
Severo, Uberlandio Batista. "Estudo de uma classe de equações de Schrodinger quase-lineares." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307293.
Анотація:
Orientadores: João Marcos Bezerra do O, Orlando Francisco LopesTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho, estudamos questões relacionadas à existência, multiplicidade e comportamento de concentração de soluções do tipo onda estacionária, para uma classe de equações de Schrödinger quase-lineares, as quais modelam fenômenos físicos, por exemplo, na F³sica de Plasmas. Na obtenção de nossos resultados, usamos métodos variacionais, tais como, teoremas do tipo mini-max, bem como, teoria de regularidade de equações elípticas de segunda ordem
Abstract: In this work, we study questions related to existence, multiplicity and concentration behavior of standing waves, for a class of quasilinear Schrödinger equations, arising, for example, in Plasma Physics. To obtain our results, we use variational methods, such as, minimax theorems and also regularity theory of elliptic equations of second order
Doutorado
Analise
Doutor em Matemática
21
Naceur, Nahed. "Une méthode de décomposition de domaine pour la résolution numérique d’une équation non-linéaire." Thesis, Université de Lorraine, 2020. http://www.theses.fr/2020LORR0149.
Анотація:
Cette thèse porte sur l’analyse théorique et la résolution numérique d’un type d’équations semi-linéaires elliptiques et paraboliques. Ces équations sont souvent utilisées pour modéliser des phénomènes dans la dynamique de la population et les réactions chimiques. On a commencé cette thèse par l’étude théorique d’une équation elliptique semi-linéaire dont on a démontré l’existence d’une solution faible non négative sous des hypothèses plus générale que celles considérées dans des précédents travaux. Puis on a présenté une nouvelle méthode basée sur la méthode de Newton et la méthode de décomposition de domaine sans et avec recouvrement. Ensuite, on a rappelé quelques aspects théoriques concernant l’existence, l’unicité ainsi que la régularité de la solution d’une équation parabolique appelée équation de type Fujita. On a rappelé aussi des résultats sur l’existence de la solution globale et sur le temps maximal d’existence dans le cas d’explosion. Afin de calculer une approximation numérique de la solution de ce type d’équation, on a introduit une discrétisation en éléments finis dans la variable en espace et un schéma de Crank-Nicholson pour la discrétisation en temps. Pour résoudre le problème non linéaire discret on a implémenté une méthode de Newton couplée avec une méthode de décomposition de domaine. On a démontré que la méthode est bien posée. On a également traité un autre type d’équation parabolique dit équation de Chipot-Weissler. En premier, on a rappelé des résultats théoriques concernant cette équation. Puis, en se basant sur les méthodes numériques étudiées précédemment on a calculé une approximation numérique de la solution de cette équation. Dans la dernière section de chaque chapitre de cette thèse on a présenté des simulations numériques illustrant les performances des algorithmes étudiés et la cohérence des résultats avec la théorieThe subject of this thesis is to present a theoretical analysis and a numerical resolution of a type of quasi-linear elliptic and parabolic equations. These equations present an important role to model phenomena in population dynamics and chemical reactions. We started this thesis with the theoretical study of a quasi-linear elliptical equation for which we demonstrated the existence of a weak non-negative solution under more general hypotheses than those considered in previous works. Then we inspired a new method based on Newton’s method and the domain decomposition method without and with overlapping. Then, we recalled some theoretical aspects concerning the existence, the uniqueness and the regularity of the solution of a parabolic equation called Fujita equation. We also recalled results about the existence of the global solution and the maximum time of existence in the case of blow-up. In order to calculate a numerical approximation of the solution of this type of equation, we introduced a finite element discretization in the space variable and a Crank-Nicholson scheme for the time discretization. To solve the discrete nonlinear problem we implemented a Newton’s method coupled with a domain decomposition method. We have shown that the method is well posed. Another type of parabolic equation known as the Chipot-Weissler equation has also been treated. First, we recalled theoretical results concerning this equation. Then, based on the numerical methods studied previously, a numerical approximation of the solution of this equation was calculated. In the last section of each chapter of this thesis we presented numerical simulations illustrating the performance of the algorithms studied and its compatibility with the theory
22
Odland, Tove. "On Methods for Solving Symmetric Systems of Linear Equations Arising in Optimization." Doctoral thesis, KTH, Optimeringslära och systemteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-166675.
Анотація:
In this thesis we present research on mathematical properties of methods for solv- ing symmetric systems of linear equations that arise in various optimization problem formulations and in methods for solving such problems. In the first and third paper (Paper A and Paper C), we consider the connection be- tween the method of conjugate gradients and quasi-Newton methods on strictly convex quadratic optimization problems or equivalently on a symmetric system of linear equa- tions with a positive definite matrix. We state conditions on the quasi-Newton matrix and the update matrix such that the search directions generated by the corresponding quasi-Newton method and the method of conjugate gradients respectively are parallel. In paper A, we derive such conditions on the update matrix based on a sufficient condition to obtain mutually conjugate search directions. These conditions are shown to be equivalent to the one-parameter Broyden family. Further, we derive a one-to-one correspondence between the Broyden parameter and the scaling between the search directions from the method of conjugate gradients and a quasi-Newton method em- ploying some well-defined update scheme in the one-parameter Broyden family. In paper C, we give necessary and sufficient conditions on the quasi-Newton ma- trix and on the update matrix such that equivalence with the method of conjugate gra- dients hold for the corresponding quasi-Newton method. We show that the set of quasi- Newton schemes admitted by these necessary and sufficient conditions is strictly larger than the one-parameter Broyden family. In addition, we show that this set of quasi- Newton schemes includes an infinite number of symmetric rank-one update schemes. In the second paper (Paper B), we utilize an unnormalized Krylov subspace frame- work for solving symmetric systems of linear equations. These systems may be incom- patible and the matrix may be indefinite/singular. Such systems of symmetric linear equations arise in constrained optimization. In the case of an incompatible symmetric system of linear equations we give a certificate of incompatibility based on a projection on the null space of the symmetric matrix and characterize a minimum-residual solu- tion. Further we derive a minimum-residual method, give explicit recursions for the minimum-residual iterates and characterize a minimum-residual solution of minimum Euclidean norm.I denna avhandling betraktar vi matematiska egenskaper hos metoder för att lösa symmetriska linjära ekvationssystem som uppkommer i formuleringar och metoder för en mängd olika optimeringsproblem. I första och tredje artikeln (Paper A och Paper C), undersöks kopplingen mellan konjugerade gradientmetoden och kvasi-Newtonmetoder när dessa appliceras på strikt konvexa kvadratiska optimeringsproblem utan bivillkor eller ekvivalent på ett symmet- risk linjärt ekvationssystem med en positivt definit symmetrisk matris. Vi ställer upp villkor på kvasi-Newtonmatrisen och uppdateringsmatrisen så att sökriktningen som fås från motsvarande kvasi-Newtonmetod blir parallell med den sökriktning som fås från konjugerade gradientmetoden. I den första artikeln (Paper A), härleds villkor på uppdateringsmatrisen baserade på ett tillräckligt villkor för att få ömsesidigt konjugerade sökriktningar. Dessa villkor på kvasi-Newtonmetoden visas vara ekvivalenta med att uppdateringsstrategin tillhör Broydens enparameterfamilj. Vi tar också fram en ett-till-ett överensstämmelse mellan Broydenparametern och skalningen mellan sökriktningarna från konjugerade gradient- metoden och en kvasi-Newtonmetod som använder någon väldefinierad uppdaterings- strategi från Broydens enparameterfamilj. I den tredje artikeln (Paper C), ger vi tillräckliga och nödvändiga villkor på en kvasi-Newtonmetod så att nämnda ekvivalens med konjugerade gradientmetoden er- hålls. Mängden kvasi-Newtonstrategier som uppfyller dessa villkor är strikt större än Broydens enparameterfamilj. Vi visar också att denna mängd kvasi-Newtonstrategier innehåller ett oändligt antal uppdateringsstrategier där uppdateringsmatrisen är en sym- metrisk matris av rang ett. I den andra artikeln (Paper B), används ett ramverk för icke-normaliserade Krylov- underrumsmetoder för att lösa symmetriska linjära ekvationssystem. Dessa ekvations- system kan sakna lösning och matrisen kan vara indefinit/singulär. Denna typ av sym- metriska linjära ekvationssystem uppkommer i en mängd formuleringar och metoder för optimeringsproblem med bivillkor. I fallet då det symmetriska linjära ekvations- systemet saknar lösning ger vi ett certifikat för detta baserat på en projektion på noll- rummet för den symmetriska matrisen och karaktäriserar en minimum-residuallösning. Vi härleder även en minimum-residualmetod i detta ramverk samt ger explicita rekur- sionsformler för denna metod. I fallet då det symmetriska linjära ekvationssystemet saknar lösning så karaktäriserar vi en minimum-residuallösning av minsta euklidiska norm.
QC 20150519
23
Filho, NarcÃlio Silva de Oliveira. "Regularidade para equaÃÃes quase lineares em conjuntos singulares degenerados." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14681.
Анотація:
FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgicoCoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
We will study a new universal gradient continuity estimate for solutions to quasi-linear equations with varying coefficients at singular set of degeneracy: S(u) := {X : Du(X) = 0}. Ourmain theorem reveals that along S(u), u is asymptotic as regular as solutions to constant coefficient equations. In particular, along the critical set S(u),u enjoys a modulus of continuity much superior than the possibly low, continuity feature of the coefficients. The results are new even in the context of linear elliptic equations, where it is herein shown that H^1- weak solutions to div (a(X,Du))= 0 with aij elliptic and dinicontinuous are actually C ^{1,1^{-}} along S(u). The results and insights of this work foster a new understanding os smoothness properties of solutions to degenerate or singular equations, beyond typical elliptic regularity estimates, precisely where the diffusion attributes of the equation collapse.
Neste trabalho estudaremos uma nova estimativa universal para a continuidade do gradiente de soluÃÃes para equaÃÃes quase lineares com coeficientes variÃveis em conjuntos singulares degenerados que serÃo denotados por S(u) := {X : Du(X) = 0} . O resultado principal deste trabalho revela que ao longo de S(u), u à assintoticamente tÃo regular quanto as soluÃÃes das equaÃÃes com coeficientes constantes. Em particular, ao longo do conjunto S(u), Du tem um mÃdulo de continuidade superior a baixa caracterÃstica de continuidade de seus coeficientes. Os resultados sÃo novos e mesmo no contexto de equaÃÃes diferenciais lineares onde se mostra que soluÃÃes H^1- fracas da equaÃÃo div(a(X, Du)) = 0 com os aij elÃpicos e Dini-ContÃnuos sÃo realmente C ^{1,1^{-}} ao longo de S(u). Os resultados e as perspectivas deste trabalho promovem um novo entendimento sobre as propriedades suavidade de soluÃÃes para equaÃÃes singulares, ou degeneradas, alÃm de estimativas tÃpicas sobre regularidade elÃpticas, precisamente onde temos os atributos de difusÃo do equaÃÃo do colapso.
24
Akanda, Md Abdus Salam. "A generalized estimating equations approach to capture-recapture closed population models: methods." Doctoral thesis, Universidade de Évora, 2014. http://hdl.handle.net/10174/18297.
Анотація:
ABSTRACT; Wildlife population parameters, such as capture or detection probabilities, and density or population size, can be estimated from capture-recapture data. These estimates are of particular interest to ecologists and biologists who rely on ac- curate inferences for management and conservation of the population of interest. However, there are many challenges to researchers for making accurate inferences on population parameters. For instance, capture-recapture data can be considered as binary longitudinal observations since repeated measurements are collected on the same individuals across successive points in times, and these observations are often correlated over time. If these correlations are not taken into account when estimating capture probabilities, then parameter estimates will be biased, possibly producing misleading results. Also, an estimator of population size is generally biased under the presence of heterogeneity in capture probabilities. The use of covariates (or auxiliary variables), when available, has been proposed as an alternative way to cope with the problem of heterogeneous capture probabilities. In this dissertation, we are interested in tackling these two main problems, (i) when capture probabilities are dependent among capture occasions in closed population capture-recapture models, and (ii) when capture probabilities are heterogeneous among individuals. Hence, the capture-recapture literature can be improved, if we could propose an approach to jointly account for these problems. In summary, this dissertation proposes: (i) a generalized estimating equations (GEE) approach to model possible effects in capture-recapture closed population studies due to correlation over time and individual heterogeneity; (ii) the corresponding estimating equations for each closed population capture-recapture model; (iii) a comprehensive analysis on various real capture-recapture data sets using classical, GEE and generalized linear mixed models (GLMM); (iv) an evaluation of the effect of ac- counting for correlation structures on capture-recapture model selection based on the ‘Quasi-likelihood Information Criterion (QIC)’; (v) a comparison of the performance of population size estimators using GEE and GLMM approaches in the analysis of capture-recapture data. The performance of these approaches is evaluated by Monte Carlo (MC) simulation studies resembling real capture-recapture data. The proposed GEE approach provides a useful inference procedure for estimating population parameters, particularly when a large proportion of individuals are captured. For a low capture proportion, it is difficult to obtain reliable estimates for all approaches, but the GEE approach outperforms the other methods. Simulation results show that quasi-likelihood GEE provide lower standard error than partial likelihood based on generalized linear modelling (GLM) and GLMM approaches. The estimated population sizes vary on the nature of the existing correlation among capture occasions; RESUMO: Parâmetros populacionais em espécies de vida selvagens, como probabilidade captura ou deteção, e abundância ou densidade da população, podem ser estimados a partir de dados de captura-recaptura. Estas estimativas são de particular interesse para ecologistas e biólogos que dependem de inferências precisas a gestão e conservação das populações. No entanto, há muitos desafios par investigadores fazer inferências precisas de parâmetros populacionais. Por exemplo, os dados de captura-recaptura podem ser considerados como observa longitudinais binárias uma vez que são medições repetidas coletadas nos mesmos indivíduos em pontos sucessivos no tempo, e muitas vezes correlacionadas. Essas correlações não são levadas em conta ao estimar as probabilidades de tura, as estimativas dos parâmetros serão tendenciosas e possivelmente produz resultados enganosos. Também, um estimador do tamanho de uma população geralmente enviesado na presença de heterogeneidade das probabilidades de captura. A utilização de co-variáveis (ou variáveis auxiliares), quando disponível tem sido proposta como uma forma de lidar com o problema de probabilidade captura heterogéneas. Nesta dissertação, estamos interessados em abordar problemas principais em mode1os de captura-recapturar para população fecha (i) quando as probabilidades de captura são dependentes entre ocasiões de captura e (ii) quando as probabilidades de captura são heterogéneas entre os indivíduos Assim, a literatura de captura-recaptura pode ser melhorada, se pudéssemos por uma abordagem conjunta para estes problemas. Em resumo, nesta dissertação propõe-se: (i) uma abordagem de estimação de equações generalizadas (GEE) para modelar possíveis efeitos de correlação temporal e heterogeneidade individual nas probabilidades de captura; (ii) as correspondentes equações de estimação generalizadas para cada modelo de captura-recaptura em população fechadas; (iii) uma análise sobre vários conjuntos de dados reais de captura-recaptura usando a abordagem clássica, GEE e modelos linear generalizados misto (GLMM); (iv) uma avaliação do efeito das estruturas de correlação na seleção de modelos de captura-recaptura com base no ‘critério de informação da Quasi-verossimilhança (QIC); (v) uma comparação da performance das estimativas do tamanho da população usando GEE e GLMM. O desempenho destas abordagens ´e avaliado usando simulações Monte Carlo (MC) que se assemelham a dados de captura- recapture reais. A abordagem GEE proposto ´e um procedimento de inferência útil para estimar parâmetros populacionais, especialmente quando uma grande proporção de indivíduos ´e capturada. Para uma proporção baixa de capturas, ´e difícil obter estimativas fiáveis para todas as abordagens aplicadas, mas GEE supera os outros métodos. Os resultados das simulações mostram que o método da quase-verossimilhança do GEE fornece estimativas do erro padrão menor do que o método da verossimilhança parcial dos modelos lineares generalizados (GLM) e GLMM. As estimativas do tamanho da população variam de acordo com a natureza da correlação existente entre as ocasiões de captura.
25
Rampasso, Giane Casari. "Soluções quase periódicas para equações diferenciais funcionais /." São José do Rio Preto, 2015. http://hdl.handle.net/11449/127744.
Анотація:
Orientador: Andréa Cristina Prokopczyk AritaBanca: German Jesus Lozada Cruz
Banca: Sandro Marcos Guzzo
Resumo: O objetivo deste trabalho e encontrar soluções fracas quase peri odicas para equações diferenciais que podem ser escritas na forma u0(t) = Au(t) + f(u(t); t); t 2 R; onde A e o gerador in nitesimal de um C0 - semigrupo exponencialmente est avel, X e um espa co de Banach e f : X R ! X e uma função apropriada. Para isto, estudaremos as principais propriedades da teoria de semigrupos de operadores lineares limitados e da teoria de fun c~oes quase peri odicas. Al em disso, apresentaremos resultados que garantem a existência e a unicidade de solução para o problema de Cauchy abstrato, utilizando como ferramenta, a teoria de semigrupos
Abstract: The purpose of this work is to nd almost periodic mild solutions for di erential equations that can be written in the form u0(t) = Au(t) + f(u(t); t); t 2 R; where A is the in nitesimal generator of a exponentially stable C0 - semigroup, X is a Banach space and f : X R ! X is an appropriate function. For this, we will study the main properties of the theory of semigroup of bounded linear operators and the theory of almost periodic functions. Moreover, we will present results that ensure the existence and uniqueness of solution for the abstract Cauchy problem, using as a tool, the semigroup theory
Mestre
26
Venezuela, Maria Kelly. ""Modelos lineares generalizados para análise de dados com medidas repetidas"." Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-07072006-122612/.
Анотація:
Neste trabalho, apresentamos as equações de estimação generalizadas desenvolvidas por Liang e Zeger (1986), sob a ótica da teoria de funções de estimação apresentada por Godambe (1991). Essas equações de estimação são obtidas para os modelos lineares generalizados (MLGs) considerando medidas repetidas. Apresentamos também um processo iterativo para estimação dos parâmetros de regressão, assim como testes de hipóteses para esses parâmetros. Para a análise de resíduos, generalizamos para dados com medidas repetidas algumas técnicas de diagnóstico usuais em MLGs. O gráfico de probabilidade meio-normal com envelope simulado é uma proposta para avaliarmos a adequação do ajuste do modelo. Para a construção desse gráfico, simulamos respostas correlacionadas por meio de algoritmos que descrevemos neste trabalho. Por fim, realizamos aplicações a conjuntos de dados reais.In this work, we consider the generalized estimation equations developed by Liang and Zeger (1986) focusing the theory of estimating functions presented by Godambe (1991). These estimation equations are an extension of generalized linear models (GLMs) to the analysis of repeated measurements. We present an iterative procedure to estimate the regression parameters as well as hypothesis testing of these parameters. For the residual analysis, we generalize to repeated measurements some diagnostic methods available for GLMs. The half-normal probability plot with a simulated envelope is useful for diagnosing model inadequacy and detecting outliers. To obtain this plot, we consider an algorithm for generating a set of nonnegatively correlated variables having a specified correlation structure. Finally, the theory is applied to real data sets.
27
Hitomi, Eduardo Eizo Aramaki 1989. "Equações parabólicas quase lineares e fluxos de curvatura média em espaços euclidianos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306218.
Анотація:
Orientador: Olivâine Santana de QueirozDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Nesta dissertação realizamos um estudo sobre o fluxo de curvatura média em espaços Euclidianos sob as perspectivas analítica e geométrica. Tratamos inicialmente da existência e regularidade de soluções em tempos pequenos de equações parabólicas quase lineares de segunda ordem em variedades Riemannianas, o que é essencial para garantirmos a existência de uma solução suave em tempo pequeno do fluxo de curvatura média. Em uma segunda parte, passamos a alguns resultados sobre o comportamento no intervalo maximal de existência de uma solução suave da hipersuperfície em evolução, por meio de equações das componentes geométricas associadas e de Princípios de Máximo. Próximo desse tempo maximal, analisamos a formação de singularidades do Tipo I por meio da Fórmula de Monotonicidade de Huisken e de rescalings, e do Tipo II por meio de uma técnica de blow-up devida a Hamilton. Em especial, reservamos o caso de curvas a um capítulo a parte e apresentamos resultados clássicos da teoria de curve-shortening flows
Abstract: In this dissertation we study the mean curvature flow in Euclidean spaces from the analytic and geometric point of view. We deal initially with short-time existence and regularity of a solution for second order quasilinear parabolic equations on Riemannian manifolds, which is essential to guarantee the short-time existence of a smooth solution to the mean curvature flow. In a second part, we present some results concerning the behavior of the evolving hypersurface close to the maximal time of existence of a smooth solution, by means of Maximum Principles and evolution equations of the associated geometric components. Close to this maximal time, we analyse the formation of singularities of Type I by means of rescalings and Huisken's Monotonicity Formula, and of Type II by means of a blow-up technique due to Hamilton. In particular, we reserve the case of curves to a separate chapter, where we present some classical results in curve-shortening flow theory
Mestrado
Matematica
Mestre em Matemática
28
Gambera, Laura Rezzieri. "Soluções quase automórficas para equações diferenciais abstratas de segunda ordem /." São José do Rio Preto, 2016. http://hdl.handle.net/11449/137973.
Анотація:
Orientador: Andréa Cristina Prokopczyk AritaBanca: Sérgio Leandro Nascimento Neves
Banca: Márcia Cristina Anderson Braz Federson
Resumo: Neste trabalho estudamos a existência de solução fraca quase automórfica para equações diferenciais abstratas de segunda ordem descritas na forma x'(t) = Ax(t) + f(t, x(t)), t real, onde x(t) pertence a X para todo t real, X é um espaço de Banach, A : D(A) C X -> X é o gerador infinitesimal de uma família cosseno fortemente contínua de operadores lineares limitados em X e f : R x X -> X é uma função apropriada
Abstract: In this work we study the existence of an almost automorphic mild solution to second order abstract differential equations given by x'(t) = Ax(t) + f(t, x(t)), t real, where x(t) lies in X for all t real, X is a Banach space, A : D(A) C X ->X is the infinitesimal generator of a strongly continuous cosine family of bounded linear operators on X and f : R x X -> X is an appropriate function
Mestre
29
Mendonça, Luziane Ferreira de. "Aceleração quase-Newton para problemas de minimização com restrições." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306668.
Анотація:
Orientadores: Vera Lucia da Rocha Lopes, Jose Mario MartinezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Sistemas de Otimalidade (ou Sistemas KKT) são sistemas formados pelas condições primais-duais estacionárias para a solução de problemas de otimização. Sob hipóteses adequadas (condições de qualificação), os minimizadores locais de um problema de minimização satisfarão as equações e inequações KKT; entretanto, infelizmente, muitos outros pontos estacionários (incluindo maximizadores) também são soluções desse sistema não linear. Por essa razão, os métodos destinados à resolução de problemas de programação não-linear fazem uso constante da estrutura de minimização, e o uso simples de métodos destinados à resolução de sistemas não-lineares podem gerar soluções espúrias. Todavia, caso o método destinado à resolução do sistema KKT tenha um ponto inicial situado na região de atração para um minimizador, esse método pode vir a ser muito eficiente. Neste trabalho, os métodos quase-Newton para a resolução de sistemas não-lineares são usados como aceleradores de algoritmos de programação não-linear (Lagrangiano Aumentado) com restrições de igualdade, desigualdade e caixa. Utilizamos como acelerador o método simétrico inverso de correção de posto um (ISR1), o qual realiza reínicios periódicos e faz uso das estruturas esparsas das matrizes para armazenamento. São demonstrados resultados de convergência e são realizados vários experimentos numéricos que comprovam a eficiência desta estratégia para problemas de minimização com restrições de igualdade, e indicam outros caminhos para problemas de minimização com restrições gerais (igualdade, desigualdade e caixa)
Abstract: Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this work quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms. A periodically-restarted memoryless symmetric rank-one (SRI) correction method is introduced for that purpose. Convergence results are given. For problems with only equality constraints, numerical experiments that confirm that the acceleration is effective are presented. A bunch of problems with equalities, inequalities and box constraints is tested and several comments and suggestions for further work are presented
Doutorado
Doutor em Matemática Aplicada
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Anjos, Hudson Umbelino dos. "Soluções para uma Classe de Equações de Schrödinger Quase Lineares via Método de Nehari." Universidade Federal da Paraíba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/7460.
Анотація:
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Previous issue date: 2010-08-25Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this dissertation, we study existence of both one-sign and nodal positive solutions (with exactly two nodal domains) for a class of quasilinear Schrödinger equations, which model physic phenomena, for example, in plasma physics. To obtain the results, it was used, mainly, the Nehari method, as well as, regularity theory of elliptic and Concentration-Compactness Principle.
Nesta dissertação, estudamos a existência de soluções positivas e mudando de sinal (tendo exatamente dois domínios nodais) para uma classe de equações de Schrödinger quase lineares, as quais modelam fenômenos físicos, por exemplo, em Física dos Plasmas. Na obtenção dos resultados, foi usado, principalmente, o método de Nehari, bem como teoria de regularidade elíptica e o Princípio de Concentração-Compacidade de P. L. Lions.
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Melo, Alison Marcelo Van Der Laan 1985. "Comportamento assintótico de uma classe de soluções da equação de meios porosos." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305903.
Анотація:
Orientador: Marcelo da Silva MontenegroDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Cientifica
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Resumo: Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital
Abstract: Note: The complete abstract is available with the full electronic digital thesis or dissertations
Mestrado
Matematica
Mestre em Matemática
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Fromm, Alexander. "Theory and applications of decoupling fields for forward-backward stochastic differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2015. http://dx.doi.org/10.18452/17115.
Анотація:
Diese Arbeit beschäftigt sich mit der Theorie der sogenannten stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDE), welche als ein stochastisches Anologon und in gewisser Weise als eine Verallgemeinerung von parabolischen quasi-linearen partiellen Differentialgleichungen betrachtet werden können. Die Dissertation besteht aus zwei Teilen: In dem ersten entwicklen wir die Theorie der sogenannten Entkopplungsfelder für allgemeine mehrdimensionale stark gekoppelte FBSDE. Diese Theorie besteht aus Existenz- sowie Eindeutigkeitsresultaten basierend auf dem Konzept des maximalen Intervalls. Es beinhaltet darüberhinaus Werkzeuge um Regularität von konkreten Problemen zu untersuchen. Insgesamt wird die Theorie für drei Klassen von Problemen entwickelt: In dem ersten Fall werden Lipschitz-Bedingungen an die Parameter des Problems vorausgesetzt, welche zugleich vom Zufall abhängen dürfen. Die Untersuchung der beiden anderen Klassen basiert auf dem ersten. In diesen werden die Parameter als deterministisch vorausgesetzt. Gleichwohl wird die Lipschitz-Stetigkeit durch zwei verschiedene Formen der lokalen Lipschitz-Stetigkeit abgeschwächt. In dem zweiten Teil werden diese abstrakten Resultate auf drei konkrete Probleme angewendet: In der ersten Anwendung wird gezeigt wie globale Lösbarkeit von FBSDE in dem sogenannten nicht-degenerierten Fall untersucht werden kann. In der zweiten Anwendung wird die Lösbarkeit eines gekoppelten Systems gezeigt, welches eine Lösung zu dem Skorokhod''schen Einbettungproblem liefert. Die Lösung wird für den Fall einer allgemeinen nicht-linearen Drift konstruiert. Die dritte Anwendung führt auf Lösbarkeit eines komplexen gekoppelten Vorwärt-Rückwärts-Systems, aus welchem optimale Strategien für das Problem der Nutzenmaximierung in unvollständingen Märkten konstruiert werden. Das System wird in einem verhältnismäßig allgmeinen Rahmen gelöst, d.h. für eine verhältnismäßig allgemeine Klasse von Nutzenfunktion auf den reellen Zahlen.This thesis deals with the theory of so called forward-backward stochastic differential equations (FBSDE) which can be seen as a stochastic formulation and in some sense generalization of parabolic quasi-linear partial differential equations. The thesis consist of two parts: In the first we develop the theory of so called decoupling fields for general multidimensional fully coupled FBSDE in a Brownian setting. The theory consists of uniqueness and existence results for decoupling fields on the so called the maximal interval. It also provides tools to investigate well-posedness and regularity for particular problems. In total the theory is developed for three different classes of FBSDE: In the first Lipschitz continuity of the parameter functions is required, which at the same time are allowed to be random. The other two classes we investigate are based on the theory developed for the first one. In both of them all parameter functions have to be deterministic. However, two different types of local Lipschitz continuity replace the more restrictive Lipschitz continuity of the first class. In the second part we apply these techniques to three different problems: In the first application we demonstrate how well-posedness of FBSDE in the so called non-degenerate case can be investigated. As a second application we demonstrate the solvability of a system, which provides a solution to the so called Skorokhod embedding problem (SEP) via FBSDE. The solution to the SEP is provided for the case of general non-linear drift. The third application provides solutions to a complex FBSDE from which optimal trading strategies for a problem of utility maximization in incomplete markets are constructed. The FBSDE is solved in a relatively general setting, i.e. for a relatively general class of utility functions on the real line.
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Li, Daoji. "Empirical likelihood and mean-variance models for longitudinal data." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/empirical-likelihood-and-meanvariance-models-for-longitudinal-data(98e3c7ef-fc88-4384-8a06-2c76107a9134).html.
Анотація:
Improving the estimation efficiency has always been one of the important aspects in statistical modelling. Our goal is to develop new statistical methodologies yielding more efficient estimators in the analysis of longitudinal data. In this thesis, we consider two different approaches, empirical likelihood and jointly modelling the mean and variance, to improve the estimation efficiency. In part I of this thesis, empirical likelihood-based inference for longitudinal data within the framework of generalized linear model is investigated. The proposed procedure takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix and retains optimality even if the working correlation structure is misspecified. The proposed approach yields more efficient estimators than conventional generalized estimating equations and achieves the same asymptotic variance as quadratic inference functions based methods. The second part of this thesis focus on the joint mean-variance models. We proposed a data-driven approach to modelling the mean and variance simultaneously, yielding more efficient estimates of the mean regression parameters than the conventional generalized estimating equations approach even if the within-subject correlation structure is misspecified in our joint mean-variance models. The joint mean-variances in parametric form as well as semi-parametric form has been investigated. Extensive simulation studies are conducted to assess the performance of our proposed approaches. Three longitudinal data sets, Ohio Children’s wheeze status data (Ware et al., 1984), Cattle data (Kenward, 1987) and CD4+ data (Kaslowet al., 1987), are used to demonstrate our models and approaches.
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Li, Ji. "Analyse mathématique de modèles d'intrusion marine dans les aquifères côtiers." Thesis, Littoral, 2015. http://www.theses.fr/2015DUNK0378/document.
Анотація:
Le thème de cette thèse est l'analyse mathématique de modèles décrivant l'intrusion saline dans les aquifères côtiers. On a choisi d'adopter la simplicité de l'approche avec interface nette : il n'y a pas de transfert de masse entre l'eau douce et l'eau salée (resp. entre la zone saturée et la zone sèche). On compense la difficulté mathématique liée à l'analyse des interfaces libres par un processus de moyennisation verticale nous permettant de réduire le problème initialement 3D à un système d'edps définies sur un domaine, Ω, 2D. Un second modèle est obtenu en combinant l'approche 'interface nette' à celle avec interface diffuse ; cette approche est déduite de la théorie introduite par Allen-Cahn, utilisant des fonctions de phase pour décrire les phénomènes de transition entre les milieux d'eau douce et d'eau salée (respectivement les milieux saturé et insaturé). Le problème d'origine 3D est alors réduit à un système fortement couplé d'edps quasi-linéaires de type parabolique dans le cas des aquifères libres décrivant l'évolution des profondeurs des 2 surfaces libres et de type elliptique-parabolique dans le cas des aquifères confinés, les inconnues étant alors la profondeur de l'interface eau salée par rapport à eau douce et la charge hydraulique de l'eau douce. Dans la première partie de la thèse, des résultats d'existence globale en temps sont démontrés montrant que l'approche couplée interface nette-interface diffuse est plus pertinente puisqu'elle permet d'établir un principe du maximum plus physique (plus précisèment une hiérarchie entre les 2 surfaces libres). En revanche, dans le cas de l'aquifère confiné, nous montrons que les deux approches conduisent à des résultats similaires. Dans la seconde partie de la thèse, nous prouvons l'unicité de la solution dans le cas non dégénéré, la preuve reposant sur un résultat de régularité du gradient de la solution dans l'espace Lr (ΩT), r > 2, (ΩT = (0,T) x Ω). Puis nous nous intéressons à un problème d'identification des conductivités hydrauliques dans le cas instationnaire. Ce problème est formulé par un problème d'optimisation dont la fonction coût mesure l'écart quadratique entre les charges hydrauliques expérimentales et celles données par le modèleThe theme of this thesis is the analysis of mathematical models describing saltwater intrusion in coastal aquifers. The simplicity of sharp interface approach is chosen : there is no mass transfer between fresh water and salt water (respectively between the saturated zone and the area dry). We compensate the mathematical difficulty of the analysis of free interfaces by a vertical averaging process allowing us to reduce the 3D problem to system of pde's defined on a 2D domain Ω. A second model is obtained by combining the approach of 'sharp interface' in that with 'diffuse interface' ; this approach is derived from the theory introduced by Allen-Cahn, using phase functions to describe the phenomena of transition between fresh water and salt water (respectively the saturated and unsaturated areas). The 3D problem is then reduced to a strongly coupled system of quasi-linear parabolic equations in the unconfined case describing the evolution of the DEPTHS of two free surfaces and elliptical-parabolic equations in the case of confined aquifer, the unknowns being the depth of salt water/fresh water interface and the fresh water hydraulic head. In the first part of the thesis, the results of global in time existence are demonstrated showing that the sharp-diffuse interface approach is more relevant since it allows to establish a mor physical maximum principle (more precisely a hierarchy between the two free surfaces). In contrast, in the case of confined aquifer, we show that both approach leads to similar results. In the second part of the thesis, we prove the uniqueness of the solution in the non-degenerate case. The proof is based on a regularity result of the gradient of the solution in the space Lr (ΩT), r > 2, (ΩT = (0,T) x Ω). Then we are interest in a problem of identification of hydraulic conductivities in the unsteady case. This problem is formulated by an optimization problem whose cost function measures the squared difference between experimental hydraulic heads and those given by the model
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Mayol, Serra Catalina. "Dinàmica no lineal de sistemes làsers: potencials de Lyapunov i diagrames de bifurcacions." Doctoral thesis, Universitat de les Illes Balears, 2002. http://hdl.handle.net/10803/9430.
Анотація:
En aquest treball s'ha estudiat la dinàmica dels làsers de classe A i de classe B en termes del potencial de Lyapunov. En el cas que s'injecti un senyal al làser o es modulin alguns dels paràmetres, apareix un comportament moltmés complex i s'estudia el conjunt de bifurcacions.1) Als làsers de classe A, la dinàmica determinista s'ha interpretat com el moviment damunt el potencial de Lyapunov. En la dinàmica estocàstica s'obté un flux sostingut per renou per a la fase del camp elèctric.
2) Per als làsers de classe A amb senyal injectat, s'ha descrit el conjunt de bifurcacions complet i s'ha determinat el conjunt d'amplituds i freqüències en el quals el làser respon
ajustant la seva freqüència a la del camp extern.
3) S'ha obtingut un potencial de Lyapunov pels làsers de classe B, només vàlid en el cas determinista, que inclou els termes de saturació de guany i d'emissió espontània.
4) S'ha realitzat un estudi del conjunt de bifurcacions parcial al voltant del règim tipus II de la singularitat Hopf--sella--node en un làser de classe B amb senyal injectat.
5) S'han identificat les respostes òptimes pels làsers de semiconductor sotmesos a modulació periòdica externa. S'han obtingut les corbes que donen la resposta màxima per cada tipus de resonància en el pla definit per l'amplitud relativa de modulació i la freqüència de modulació.
In this work we have studied the dynamics of both class A and class B lasers in terms of Lyapunov potentials. In the case of an injected signal or when some laser parameters are modulated, and more complex behaviour is expected, the bifurcation set is studied. The main results are the following:
1) For class A lasers, the deterministic dynamics has been interpreted as a movement on the potential landscape. In the stochastic dynamics we have found a noise sustained flow for the phase of the electric field.
2) For class A lasers with an injected signal, we have been able to describe the whole bifurcation set of this system and to determine the set of amplitudes frequencies for which the laser responds adjusting its frequency to that of the external field.
3) In the case of class B lasers, we have obtained a Lyapunov potential only valid in the deterministic case, including spontaneous emission and gain saturation terms. The fixed point corresponding to the laser in the on state has been interpreted as a minimum in this potential. Relaxation to this minimum is reached through damped oscillations.
4) We have performed a study of the partial bifurcation set around the type II regime of the Hopf-saddle-node singularity in a class B laser with injected signal.
5) We have identified the optimal responses of a semiconductor laser subjected to an external periodic modulation. The lines that give a maximum response for each type of resonance are obtained in the plane defined by the relative amplitude modulation and frequency modulation.
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Luo, Tingjian. "Existence non existence et multiplicité d'ondes stationnaires normalisées pour quelques équations non linéaires elliptiques." Phd thesis, Université de Franche-Comté, 2013. http://tel.archives-ouvertes.fr/tel-01061670.
Анотація:
Dans cette thèse, nous étudions l'existence, non existence et multiplicité des ondes stationnairesavec les normes prescrites pour deux types d'équations aux dérivées partiellesnon linéaires elliptiques découlant de différents modèles physiques. La stabilité orbitale desondes stationnaires est également étudiée dans certains cas. Les principales méthodes denos preuves sont des arguments variationnels. Les solutions sont obtenues comme pointscritiques de fonctionnelle associée sur une contrainte.La thèse se compose de sept chapitres. Le Chapitre 1 est l'introduction de la thèse. Dansles Chapitres 2 à 4, nous étudions une classe d'équations de Schrödinger-Poisson-Slaternon linéaires. Nous établissons dans le Chapitre 2 des résultats optimaux non existencede solutions d'énergie minimale ayant une norme L2 prescrite. Dans le Chapitre 3, nousmontrons un résultat d'existence de solutions L2 normalisées, dans une cas où la fonctionnelleassociée n'est pas bornée inférieurement sur la contrainte. Nos solutions sonttrouvées comme des points de selle de la fonctionnelle, mais ils correspondent à des solutionsd'énergée minimale. Nous montrons également que les ondes stationnaires associéessont orbitalement instables. Ici, puisque nos points critiques présumés ne sont pas desminimiseurs globaux, il n'est pas possible d'utiliser de façon systématique les méthodesde compacité par concentration développées par P. L. Lions. Ensuite, dans le Chapitre4, nous montrons que sous les hypothèses du Chapitre 3, il existe une infinité de solutionsayant une norme L2 prescrite. Dans les deux chapitres suivants, nous étudions uneclasse d'équations de Schrödinger quasi-linéaires. Des résultats optimaux non existence desolutions d'énergie minimale sont donnés dans le Chapitre 5. Dans le Chapitre 6, nousprouvons l'existence de deux solutions positives ayant une norme donnée. L'une d'elles,relativement à la contrainte L2, est de type point selle. L'autre est un minimum, soit localou global. Le fait que la fonctionnelle naturelle associée à cette équation n'est pas biendéfinie nécessite l'utilisation d'une méthode de perturbation pour obtenir ces deux pointscritiques. Enfin, au Chapitre 7, nous mentionnons quelques questions que cette thèse asoulevées.
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Bringmann, Philipp. "Adaptive least-squares finite element method with optimal convergence rates." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22350.
Анотація:
Die Least-Squares Finite-Elemente-Methoden (LSFEMn) basieren auf der Minimierung des Least-Squares-Funktionals, das aus quadrierten Normen der Residuen eines Systems von partiellen Differentialgleichungen erster Ordnung besteht. Dieses Funktional liefert einen a posteriori Fehlerschätzer und ermöglicht die adaptive Verfeinerung des zugrundeliegenden Netzes. Aus zwei Gründen versagen die gängigen Methoden zum Beweis optimaler Konvergenzraten, wie sie in Carstensen, Feischl, Page und Praetorius (Comp. Math. Appl., 67(6), 2014) zusammengefasst werden. Erstens scheinen fehlende Vorfaktoren proportional zur Netzweite den Beweis einer schrittweisen Reduktion der Least-Squares-Schätzerterme zu verhindern. Zweitens kontrolliert das Least-Squares-Funktional den Fehler der Fluss- beziehungsweise Spannungsvariablen in der H(div)-Norm, wodurch ein Datenapproximationsfehler der rechten Seite f auftritt. Diese Schwierigkeiten führten zu einem zweifachen Paradigmenwechsel in der Konvergenzanalyse adaptiver LSFEMn in Carstensen und Park (SIAM J. Numer. Anal., 53(1), 2015) für das 2D-Poisson-Modellproblem mit Diskretisierung niedrigster Ordnung und homogenen Dirichlet-Randdaten. Ein neuartiger expliziter residuenbasierter Fehlerschätzer ermöglicht den Beweis der Reduktionseigenschaft. Durch separiertes Markieren im adaptiven Algorithmus wird zudem der Datenapproximationsfehler reduziert.
Die vorliegende Arbeit verallgemeinert diese Techniken auf die drei linearen Modellprobleme das Poisson-Problem, die Stokes-Gleichungen und das lineare Elastizitätsproblem. Die Axiome der Adaptivität mit separiertem Markieren nach Carstensen und Rabus (SIAM J. Numer. Anal., 55(6), 2017) werden in drei Raumdimensionen nachgewiesen. Die Analysis umfasst Diskretisierungen mit beliebigem Polynomgrad sowie inhomogene Dirichlet- und Neumann-Randbedingungen. Abschließend bestätigen numerische Experimente mit dem h-adaptiven Algorithmus die theoretisch bewiesenen optimalen Konvergenzraten.The least-squares finite element methods (LSFEMs) base on the minimisation of the least-squares functional consisting of the squared norms of the residuals of first-order systems of partial differential equations. This functional provides a reliable and efficient built-in a posteriori error estimator and allows for adaptive mesh-refinement. The established convergence analysis with rates for adaptive algorithms, as summarised in the axiomatic framework by Carstensen, Feischl, Page, and Praetorius (Comp. Math. Appl., 67(6), 2014), fails for two reasons. First, the least-squares estimator lacks prefactors in terms of the mesh-size, what seemingly prevents a reduction under mesh-refinement. Second, the first-order divergence LSFEMs measure the flux or stress errors in the H(div) norm and, thus, involve a data resolution error of the right-hand side f. These difficulties led to a twofold paradigm shift in the convergence analysis with rates for adaptive LSFEMs in Carstensen and Park (SIAM J. Numer. Anal., 53(1), 2015) for the lowest-order discretisation of the 2D Poisson model problem with homogeneous Dirichlet boundary conditions. Accordingly, some novel explicit residual-based a posteriori error estimator accomplishes the reduction property. Furthermore, a separate marking strategy in the adaptive algorithm ensures the sufficient data resolution. This thesis presents the generalisation of these techniques to three linear model problems, namely, the Poisson problem, the Stokes equations, and the linear elasticity problem. It verifies the axioms of adaptivity with separate marking by Carstensen and Rabus (SIAM J. Numer. Anal., 55(6), 2017) in three spatial dimensions. The analysis covers discretisations with arbitrary polynomial degree and inhomogeneous Dirichlet and Neumann boundary conditions. Numerical experiments confirm the theoretically proven optimal convergence rates of the h-adaptive algorithm.
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Cruz, Janisson Fernandes Dantas da. "Semigrupos, Automorficidade e Ergodicidade para equações de evolução semilineares." Universidade Federal de Sergipe, 2013. https://ri.ufs.br/handle/riufs/5823.
Анотація:
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESIn this work, we first develop a brief theoretical approach of semigroups of bounded linear operators, culminating on Hille-Yosida Theorem. Then we used the extrapolation theory to study su cient conditions to obtain existence and uniqueness of Almost Automorphic and Pseudo-Almost Automorphic mild solutions, through the Banach's Fixed Point Theorem for the semilinear evolution equation x(t) = Ax(t) + f(t; x(t)); t E R, where A : D(A) X ! X is a Hille-Yosida operator of negative type and not necessary dense domain on the Banach space X.
Neste trabalho, desenvolvemos inicialmente uma breve abordagem te orica dos semigrupos de operadores lineares limitados, culminando no Teorema de Hille-Yosida. Em seguida, usamos a teoria de extrapolação a fim de estudar condições suficientes para obtermos a existência e a unicidade de soluções brandas Quase Automórficas e Pseudo-quase Automórficas, por meio do Teorema do Ponto Fixo de Banach, para a equação de evolução semilinear x(t) = Ax(t) + f(t; x(t)); t E R, onde A : D(A) X ! X é um operador de Hille-Yosida de tipo negativo e dom ínio não necessariamente denso, definido no espaço de Banach X.
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Wei, Tzer-jen, and 魏澤人. "Bridge Principle of Quasi-Linear Elliptic Equation." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/73891523393028840490.
Анотація:
碩士國立臺灣大學
數學系
86
This paper give some Bridge Principle of Quasi-Linear PDE, like Bridge Principle which was often used on minimal surface or harmonic map.In this Paper , We have two theorem about in which condition, the PDE , domain , and the soution will have Bridge Principle.The first Theorem is for general Quasi-Linear and can applied to minimal surface but need much strong condition.The Second Theorem is for special type of PDE but only need weaker condition.
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Ling, Liao Wan, and 廖婉伶. "The Composite Assessment in the Quasi-experiment Research of The One-Variable Linear Equation for Middle School Students." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/77029166803593176773.
Анотація:
碩士國立臺中教育大學
數學教育學系在職進修教學碩士學位班
99
This research discusses Composite Assessment in the teaching application. Firstly,the Middle School Students taught the One-Variable Linear Equation in the Composite Assessment will be discussed in difference situation of their learning attitudes and learning achievement.In addition, the experiment group’s learning feeling are also investigated. This research adopts the Quasi-experiment design. The teacher is the researcher.Two classes at a junior high school which is in Taichung were selected as the research sample for this study.One class is the experiment group adopting the Composite Assessmen and the other is the control group adopting the traditional teaching. The research period lasted for five weeks.At the end of the experiment,Compared with two group of students in of the One-Variable Linear Equation difference situation of their learning attitudes and learning achievement.Furthermore,the research results are proceed with quantitative and qualitative modes by analysing learning journals,feedback schedulesand interviews.The research results are as follows： 1. Difference situation of learning attitudes. The experiment group and the control group in their learning attitudes have not reached the level of significance. However, the learning attitudes posttests,the experiment higher group have reached the level of significance.The average score of the first measured in experiment mediocre group achievers perform better than the latter measured. 2. Difference situation of learning achievement. The experiment group and the control group in their learning achievement have not reached the level of significance.However, when sitting for the learning achievement posttests, the experiment higher, mediocre and low group achievers perform better than the control group. 3. The feeling aspect of the the experiment group In view of the Composite Assessment in the teaching. The majority of the experiment group have expressed that they liked the experimental teaching of composite assessment.And Majority experimen group students agreed that such a teaching approach can be adopted more often in the future.
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Steinbrecher, Andreas [Verfasser]. "Numerical solution of quasi-linear differential-Algebraic equations and industrial simulation of multibody systems / vorgelegt von Andreas Steinbrecher." 2006. http://d-nb.info/980015936/34.
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"A stable manifold theorem for the gradient flow of geometric variational problems associated with a quasi-linear parabolic equations." Thesis, 1991. http://hdl.handle.net/2237/6587.
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Naito, Hisashi, and 久資 内藤. "A stable manifold theorem for the gradient flow of geometric variational problems associated with a quasi-linear parabolic equations." Thesis, 1991. http://hdl.handle.net/2237/6587.
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Sotáková, Martina. "Zobecněné odhadovací rovnice (GEE)." Master's thesis, 2020. http://www.nusl.cz/ntk/nusl-434538.
Анотація:
In this thesis we are interested in generalized estimating equations (GEE). First, we introduce the term of generalized linear model, on which generalized estimating equations are based. Next we present the methos of pseudo maximum likelyhood and quasi-pseudo maximum likelyhood, from which we move on to the methods of generalized estimating equations. Finally, we perform simulation studies, which demonstrates the theoretical results presented in the thesis. 1
45
Langer, Stefan. "Preconditioned Newton methods for ill-posed problems." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B396-D.