Relevant bibliographies by topics / Quasi Linear Equation

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Quasi Linear Equation'

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Published: 27 January 2023

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Journal articles on the topic "Quasi Linear Equation"

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Yermachenko, I. "MULTIPLE SOLUTIONS OF THE FOURTH‐ORDER EMDEN‐FOWLER EQUATION." Mathematical Modelling and Analysis 11, no. 3 (September 30, 2006): 347–56. http://dx.doi.org/10.3846/13926292.2006.9637322.

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Two-point boundary value problems for the fourth-order Emden-Fowler equation are considered. If the given equation can be reduced to a quasi‐linear one with a non‐resonant linear part so that both equations are equivalent in some domain D, and if solution of the quasi‐linear problem is located in D, then the original problem has a solution. We show that a quasi‐linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.
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FRICKE, J. ROBERT. "QUASI-LINEAR ELASTODYNAMIC EQUATIONS FOR FINITE DIFFERENCE SOLUTIONS IN DISCONTINUOUS MEDIA." Journal of Computational Acoustics 01, no. 03 (September 1993): 303–20. http://dx.doi.org/10.1142/s0218396x93000160.

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The linear elastodynamic equations are ill-posed for models which contain high contrast density discontinuities. This paper presents a quasi-linear superset of the linear equations that is well-posed for this situation. The extended system contains a conservation of mass equation and a quasi-linear convective term in the momentum equation. Density, momentum, and stress are the field variables in the quasi-linear system, which is cast in a first order form. Using a Lax–Wendroff finite difference approximation, the utility of the quasi-linear system is demonstrated by modeling underwater acoustic scattering from a truncated ice sheet. The model contains air, ice, and water with a density contrast between air and ice or water of O(103). Superlinear convergence of the Lax–Wendroff scheme is demonstrated for his heterogeneous medium problem.
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Everitt, W. N. "A note on linear ordinary quasi-differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 1-2 (1985): 1–14. http://dx.doi.org/10.1017/s0308210500026111.

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SynopsisThe theory of differential equations is largely concerned with properties of solutions of individual, or classes of, equations. This paper is given over to the converse problem - that of seeking properties of functions which require them to be, in some respect, solutions of a differential equation, and to determining all possible such differential equations.From this point of view this paper discusses only linear ordinary quasi-differential equations of the second order. However, the methods can be extended to quasi-differential equations of general order.
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Sun, Yingte, and Xiaoping Yuan. "Quasi-periodic solution of quasi-linear fifth-order KdV equation." Discrete & Continuous Dynamical Systems - A 38, no. 12 (2018): 6241–85. http://dx.doi.org/10.3934/dcds.2018268.

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Fu, Zhongjun, Jianyu Wang, Yun Ou, Genyuan Zhou, and Xiaorong Zhao. "A Linear-Correction Algorithm for Quasi-Synchronous DFT." Mathematical Problems in Engineering 2018 (December 27, 2018): 1–9. http://dx.doi.org/10.1155/2018/1268905.

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Spectral leakage in the harmonic measured by quasi-synchronous DFT (QSDFT) is mainly due to short-range leakage caused by deviation in the signal frequency. By analysing the short-range-leakage characteristic of QSDFT, a linear-correction algorithm (LCQS) for QSDFT’s harmonic-analysis results is proposed. LCQS contains two linear-correction equations: an amplitude-correction equation and an initial-phase-angle-correction equation. The former is constructed by the least-squares method, whereas the latter is generated based on the linear error characteristic of the QSDFT harmonic phase. Simulation and experimental results indicate that this proposed algorithm can efficiently increase the accuracy of the harmonic parameters over a wide frequency range by minimizing the short-range spectral leakage.
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Catino, Francesco, and Maria Maddalena Miccoli. "Construction of quasi-linear left cycle sets." Journal of Algebra and Its Applications 14, no. 01 (September 10, 2014): 1550001. http://dx.doi.org/10.1142/s0219498815500012.

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In this paper, we produce a method to construct quasi-linear left cycle sets A with Rad (A) ⊆ Fix (A). Moreover, among these cycle sets, we give a complete description of those for which Fix (A) = Soc (A) and the underlying additive group is cyclic. Using such cycle sets, we obtain left non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation which are different from those obtained in [P. Etingof, T. Schedler and A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209; P. Etingof, A. Soloviev and R. Guralnick, Indecomposable set-theoretical solutions to the quantum Yang–Baxter equation on a set with a prime number of elements, J. Algebra 242 (2001) 709–719].
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Pivovarov, Michail L. "Steady-state solutions of Minorsky’s quasi-linear equation." Nonlinear Dynamics 106, no. 4 (October 7, 2021): 3075–89. http://dx.doi.org/10.1007/s11071-021-06944-9.

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Maia, L. A., J. C. Oliveira Junior, and R. Ruviaro. "A quasi-linear Schrödinger equation with indefinite potential." Complex Variables and Elliptic Equations 61, no. 4 (January 18, 2016): 574–86. http://dx.doi.org/10.1080/17476933.2015.1106483.

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Dikhaminjia, N., J. Rogava, and M. Tsiklauri. "Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation." Journal of Mathematical Sciences 218, no. 6 (September 28, 2016): 737–41. http://dx.doi.org/10.1007/s10958-016-3058-9.

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Belokursky, M. S. "Periodic and almost periodic solutions of the Riccati equations with linear reflecting function." Doklady of the National Academy of Sciences of Belarus 66, no. 5 (November 2, 2022): 479–88. http://dx.doi.org/10.29235/1561-8323-2022-66-5-479-488.

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The method of Mironenko’s reflecting function is used for investigation of Riccati equations. The class of Riccati equations with certain-type reflecting function has been preliminarily constructed. The necessary and sufficient conditions, under which the Riccati equation would have a reflecting function linear in phase variable, are proved. These conditions are constructive in nature, since on their basis the formula is obtained, which shows the linear in phase variable reflecting function in terms of the coefficients of the Riccati equation. Additionally, the relationship between the parity (oddness) property of the coefficients of the Riccati equation and the existence of a reflecting function linear in phase variable is investigated. The application of the method of Mironenko’s reflecting function to the constructed class of Riccati equations revealed sufficient conditions, under which all its solutions are periodic or almost periodic. A sign of no periodic solutions for almost periodic Riccati equations is obtained. An example of the quasi-periodic Riccati equation with quasi-periodic reflecting function, which has a periodic solution, is given.
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Dissertations / Theses on the topic "Quasi Linear Equation"

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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.

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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.

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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'approximation
In 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
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Mokrane, Abdelhafid. "Existence de solutions pour certains problèmes quasi linéaires elliptiques et paraboliques." Paris 6, 1986. http://www.theses.fr/1986PA066086.

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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.
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Maach, Fatna. "Existence pour des systèmes de réaction-diffusion ou quasi linéaires avec loi de balance." Nancy 1, 1994. http://www.theses.fr/1994NAN10121.

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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
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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.

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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

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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.

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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 2m
This 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
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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.

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Furlan, Marco. "Structures contrôlées pour les équations aux dérivées partielles." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED008/document.

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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 GR
The 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
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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.

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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.

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Orientadores: João Marcos Bezerra do O, Djairo Guedes de Figueiredo
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-15T15:20:37Z (GMT). No. of bitstreams: 1 Moraes_ElisandradeFatimaGlossde_D.pdf: 1261630 bytes, checksum: 516f800553b6eff1f3462fe4be134e8a (MD5) Previous issue date: 2010
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
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Books on the topic "Quasi Linear Equation"

1

Delort, Jean-Marc. Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres. Providence, Rhode Island: American Mathematical Society, 2014.

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(Albert), Milani A., ed. Linear and quasi-linear evolution equations in Hilbert spaces. Providence, R.I: American Mathematical Society, 2012.

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Ninul, Anatolij Sergeevič. Tenzornaja trigonometrija: Teorija i prilozenija / Theory and Applications /. Moscow, Russia: Mir Publisher, 2004.

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Ninul, Anatolij Sergeevič. Tensor Trigonometry. Moscow, Russia: Fizmatlit Publisher, 2021.

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Ladyzhenskaia, Olga Aleksandrovna. Linear and Quasi-linear Equations of Parabolic Type. American Mathematical Society, 1995.

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Beyer, Horst Reinhard. Beyond Partial Differential Equations: On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations. Springer London, Limited, 2007.

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Beyond Partial Differential Equations: On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations (Lecture Notes in Mathematics). Springer, 2007.

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Orban, Dominique, and Mario Arioli. Iterative Solution of Symmetric Quasi-Definite Linear Systems. Society for Industrial and Applied Mathematics, 2017.

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Zeitlin, Vladimir. Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0007.

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The chapter contains the mathematical background necessary to understand the properties of RSW models and numerical methods for their simulations. Mathematics of RSW model is presented by using their one-dimensional reductions, which are necessarily’one-and-a-half’ dimensional, due to rotation and include velocity in the second direction. Basic notions of quasi-linear hyperbolic systems are recalled. The notions of weak solutions, wave breaking, and shock formation are introduced and explained on the example of simple-wave equation. Lagrangian description of RSW is used to demonstrate that rotation does not prevent wave-breaking. Hydraulic theory and Rankine–Hugoniot jump conditions are formulated for RSW models. In the two-layer case it is shown that the system loses hyperbolicity in the presence of shear instability. Ideas of construction of well-balanced (i.e. maintaining equilibria) shock-resolving finite-volume numerical methods are explained and these methods are briefly presented, with illustrations on nonlinear evolution of equatorial waves.
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Book chapters on the topic "Quasi Linear Equation"

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Epstein, Marcelo. "The Second-Order Quasi-linear Equation." In Partial Differential Equations, 115–30. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55212-5_6.

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D’Epifanio, Giulio. "About a Type of Quasi Linear Estimating Equation Approach." In Classification and Multivariate Analysis for Complex Data Structures, 253–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13312-1_26.

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Coulibaly, Ibrahim, and Christian Lécot. "Monte Carlo and quasi-Monte Carlo algorithms for a linear integro-differential equation." In Monte Carlo and Quasi-Monte Carlo Methods 1996, 176–88. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1690-2_10.

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Müller-Gronbach, Thomas, Klaus Ritter, and Tim Wagner. "Optimal Pointwise Approximation of a Linear Stochastic Heat Equation with Additive Space-Time White Noise." In Monte Carlo and Quasi-Monte Carlo Methods 2006, 577–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-74496-2_34.

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Fiorini, Camilla, Pierre-Marie Boulvard, Long Li, and Etienne Mémin. "A Two-Step Numerical Scheme in Time for Surface Quasi Geostrophic Equations Under Location Uncertainty." In Mathematics of Planet Earth, 57–67. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_5.

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AbstractIn this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations, which is then used in a multi-step method. The SQG system considered here consists of one stochastic partial differential equation, which models the stochastic transport of the buoyancy, and a linear operator linking the velocity and the buoyancy. In the LU setting, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time, based on a Milstein-type scheme in a multi-step framework. First we compared different kinds of Milstein schemes. The scheme with the best performance is then included in the two-step scheme. Finally, we show how our two-step scheme decreases the error in comparison to other multi-step schemes.
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Chen, Botao, and Yongsheng Mi. "Global Existence and Blow-up for the Quasi-Linear Parabolic Equation with Nonlinear Boundary Condition." In Lecture Notes in Electrical Engineering, 1236–40. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2386-6_163.

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Marin, Marin, and Andreas Öchsner. "Quasi-linear Equations." In Complements of Higher Mathematics, 209–22. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74684-5_6.

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Borsuk, Mikhail. "The Robin Problem for Quasi-Linear Elliptic Equation p(x)-Laplacian in a Domain with Conical Boundary Point." In Trends in Mathematics, 231–39. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87502-2_23.

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Resseguier, Valentin, Erwan Hascoët, and Bertrand Chapron. "Random Ocean Swell-Rays: A Stochastic Framework." In Mathematics of Planet Earth, 259–71. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_16.

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AbstractOriginating from distant storms, swell systems radiate across all ocean basins. Far from their sources, emerging surface waves have low steepness characteristics, with very slow amplitude variations. Swell propagation then closely follows principles of geometrical optics, i.e. the eikonal approximation to the wave equation, with a constant wave period along geodesics, when following a wave packet at its group velocity. The phase averaged evolution of quasi-linear wave fields is then dominated by interactions with underlying current and/or topography changes. Comparable to the propagation of light in a slowly varying medium, over many wavelengths, cumulative effects can lead to refraction, i.e. change of the direction of propagation of a given wave packet, so that it departs from its initial ray-propagation direction. This opens the possibility of using surface swell systems as probes to estimate turbulence along their propagating path.
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DiBenedetto, Emmanuele. "Quasi-Linear Equations of First-Order." In Partial Differential Equations, 225–63. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4552-6_8.

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Conference papers on the topic "Quasi Linear Equation"

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Wang, Yi. "Reducibility of a 1D linear beam equation with a quasi-periodic perturbation." In Fifth International Conference on Machine Vision (ICMV 12), edited by Yulin Wang, Liansheng Tan, and Jianhong Zhou. SPIE, 2013. http://dx.doi.org/10.1117/12.2013906.

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Cao, Jianbing, and Baolin Ma. "On the Stability of a Linear Functional Equation in Generalized quasi-Banach Spaces." In 2010 International Conference on Computing, Control and Industrial Engineering. IEEE, 2010. http://dx.doi.org/10.1109/ccie.2010.214.

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Dikhaminjia, N., J. Rogava, M. Tsiklauri, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Construction and Numerical Realization of Decomposition Scheme for Multidimensional Quasi-Linear Evolution Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636958.

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Barnaś, Dawid, and Lesław K. Bieniasz. "SSE-based Thomas algorithm for quasi-block-tridiagonal linear equation systems, optimized for small dense blocks." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992711.

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KULKARNI, SIDDHESH S., KAMRAN A. KHAN, and REHAN UMER. "QUASI-LINEAR VISCOELASTIC MODELLING OF UNCURED PREPREGS UNDER COMPACTION." In Thirty-sixth Technical Conference. Destech Publications, Inc., 2021. http://dx.doi.org/10.12783/asc36/35952.

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Reinforcement compaction sometimes referred as consolidation process and is one of the key steps in various composite manufacturing processes such as autoclave and out-of-autoclave processing. The prepregs consist of semi-cured thermoset resin system impregnating the fibers. hence, the prepreg shows strong viscoelastic compaction response, which strongly depends on compaction speed and stress relaxation. modeling of time-dependent response is of utmost importance to understand the behavior of prepregs during different stages of composites manufacturing processes. The quasilinear viscoelastic (QLV) theory has been extensively used for the modeling of viscoelastic response of soft tissues in biomedical applications. In QLV approach, the stress relaxation can be expressed in terms of the nonlinear elastic function and the reduced relaxation function. The constitutive equation can be represented by a convolution integral of the nonlinear strain history, and reduced relaxation function. This study adopted a quasilinear viscoelastic modeling approach to describe the time dependent behavior of uncured-prepregs under compression. The model was modified to account for the compaction behavior of the prepreg under a compressive load. The deformation behavior of the prepreg is usually characterized by the fiber volume fraction, V . In this study, the material used was a 2/2 Twill weave glass prepreg (M26T) supplied by Hexcel® Industries USA. We performed a compaction experiment of the uncured prepreg at room temperature at different displacement rate and subsequent relaxation to describe the viscoelastic behavior of the prepreg. The model parameter calibration was performed using the trust-region-reflective algorithm in matlab to a selected number of test data. The calibrated model was then used to predict the rate dependent compaction and relaxation response of prepregs for different fiber volume fractions and strain rates.
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Sharma, Ashu, and Subhash C. Sinha. "An Approximate Analysis of Quasi-Periodic Systems via Floquét Theory." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68041.

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Parametrically excited systems are generally represented by a set of linear/nonlinear ordinary differential equations with time varying coefficients. In most cases, the linear systems have been modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. Although Floquét theory is applicable only to periodic systems, it is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to two typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are extremely close to the exact boundaries of the original quasi-periodic equations. The exact boundaries are detected by computing the maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. The coefficients of the parametric excitation terms are not necessarily small in all cases. ‘Instability loops’ or ‘Instability pockets’ that appear in the stability diagram of Meissner’s equation are also observed in one case presented here. The proposed approximate approach would allow one to construct Lyapunov-Perron (L-P) transformation matrices that reduce quasi-periodic systems to systems whose linear parts are time-invariant. The L-P transformation would pave the way for controller design and bifurcation analysis of quasi-periodic systems.
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Kristyan, Sandor. "Quasi-Linear buildup of Coulomb integrals via the coupling strength parameter in the non-relativistic electronic schrödinger equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026479.

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Langner, W. J. "Sensitivity Analysis and Optimization of Mechanical System Design." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0022.

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Abstract The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.
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Tubaldi, Eleonora, Giovanni Ferrari, Prabakaran Balasubramanian, Ivan Breslavskyi, and Marco Amabili. "Viscoelastic Characterization of Woven Dacron for Aortic Grafts by Using Direction-Dependent Quasi-Linear Viscoelasticity." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87806.

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In case of direction-dependent viscoelasticity, a simplified formulation of the three-dimensional quasi-linear viscoelasticity has been obtained manipulating the original Fung equation. The experimental characterization of the static hyperelastic behaviour, the relaxation, the dynamic modulus and the loss factor of woven Dacron from a commercial aortic prosthesis has been performed. An 11 % difference of the reduced relaxation (after infinite time) between axial and circumferential directions has been observed for the woven Dacron. A very large increase in stiffness is obtained in case of harmonic loading with respect to the static loading. These findings are particularly relevant for dynamic modelling of currently used aortic grafts.
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Jasak, Hrvoje, and Gregor Cvijetić. "Implementation and Validation of the Harmonic Balance Method for Temporally Periodic Non–Linear Flows." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56254.

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An efficient method for tackling non-linear, temporally–periodic incompressible flows is presented in this paper. Assuming temporally fully periodic flow, Harmonic Balance method deploys Fourier transformation in order to formulate transient problem as a multiple quasi-steady state problems. The method is implemented in OpenFOAM and developed for a general transport equation and incompressible Navier–Stokes equations. Validation is presented on three test cases: oscillating scalar case for scalar transport validation, a flow around a 2D NACA airfoil and a 3D Onera M6 wing for turbulent incompressible Navier–Stokes validation. For all test cases Harmonic Balance results are compared to transient simulation results. Verification of the model is performed by changing the number of harmonics for all test cases.
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Reports on the topic "Quasi Linear Equation"

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Rundell, William, and Michael S. Pilant. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada256012.

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Pilant, Michael S., and William Rundell. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1989. http://dx.doi.org/10.21236/ada218462.

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