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Dissertations / Theses on the topic 'Semi linear equation'
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Michalk, Linda [Verfasser]. "Semi-Analytical Semi-Lagrangian Discontinuous Galerkin Advection Scheme for the Compressible Linear Advection Equation / Linda Michalk." Berlin : Freie Universität Berlin, 2018. http://d-nb.info/1176707140/34.
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Oswald, Luc. "Etude de problemes non lineaires avec singularites." Paris 6, 1987. http://www.theses.fr/1987PA066060.
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Cette these est composee de dix articles que nous avons regroupes en deux parties. La premiere partie est constituee par l'etude et la classification des singularites isolees, premierement, d'une equation elliptique avec diffusion, deuxiemement, de l'equation parabolique correspondante. Dans la seconde partie sont etablis des resultats d'existence pour des problemes elliptiques semi-lineaires. Ces problemes sont caracterises respectivement, par une non-linearite singuliere, une condition de neumann degeneree, une non-linearite sous lineaire et, enfin, des exposants de sobolev critiques
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Bouchitte, Guy. "Calcul des variations en cadre non reflexif : representation et relaxation de fonctionnelles integrales sur un espace de mesures, applications en plasticite et homogeneisation." Perpignan, 1987. http://www.theses.fr/1987PERP0033.
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Etude variationnelle de fonctionnelles convexes du type somomega f(x,u(x),du)dx lorsque la croissance de f necessite du travail dans un banach non reflexif. On abordera en particulier les questions relatives a la semi-continuite inferieure, la relaxation, la convergence variationnelle et l'approximation, l'equation d'euler. . . Ayant en vue certaines applications dans le dommaine de la mecanique (plasticite, milieux fissures), on s'interessera principalement au cas ou l'integrande f presente une croissance lineaire par rapport au gradient. Suivant une demarche desormais classique, cela nous amenera a etendre la definition de la fonctionnelle a des fonctions dont le gradient est une mesure bornee (espaces de type bv(omega ) ou bd(omega ). Dans cette optique, une contribution substanstielle est apportee (chapitres ii et iii notamment) au probleme de la relaxation sur un espace de mesures d'une fonctionnelle integrale dependant du parametre. Les 3 derniers chapitres ont une connotation beaucoup plus "appliquee" et sont consacres a quelques problemes d'homogeneisation et d'analyse limite issus des equations de la plasticite (chapitre v) ou de l'etude des phenomenes de diffraction en electromagnetisme (chapitre vi et vii)
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Bui, Tang Bao Ngoc. "Semi-linear waves with time-dependent speed and dissipation." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-147037.
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The main goal of our thesis is to understand qualitative properties of solutions to the Cauchy problem for the semi-linear wave model with time-dependent speed and dissipation. We greatly benefited from very precise estimates for the corresponding linear problem in order to obtain the global existence (in time) of small data solutions. This reason motivated us to introduce very carefully a complete description for classification of our models: scattering, non-effective, effective, over-damping. We have considered those separately.
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Cherfils, Laurence. "Méthode de cheminement adaptative pour les problèmes semi-linéaires dépendant d'un paramètre." Université Joseph Fourier (Grenoble), 1996. http://www.theses.fr/1996GRE10105.
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Ce travail consiste en l'élaboration d'une méthode de cheminement, dite également méthode de continuation, destinée aux problèmes de bifurcation qui apparaîssent lors de la discrétisation par éléments finis P1 d'une EDP semi-linéaire dépendant d'un paramètre. Afin de construire une méthode suffisamment robuste pour traiter les problèmes dont les solutions présentent des phénomènes de couches limites ou de singularités, nous avons intégré à la méthode de cheminement introduite par E. L. Allgower et K. Georg des techniques d'éléments finis adaptatifs, ainsi qu'une implémentation parallèle sur un réseau de stations, afin de diminuer les besoins en place mémoire et le temps de calculs nécessaires à l'évaluation d'une branche entière de solutions de bonne précision. Dans le cas de problèmes mono-dimensionnels, des essais sont effectués pour améliorer la qualité de la solution en déplaçant les nœuds du maillage, afin d'éviter le recours au raffinement. Enfin, sur un exemple où la singularité des solutions est dûe à la géométrie du domaine sur lequel est posé l'EDP, nous montrons comment l'utilisation d'un maillage «adapté à la singularité» permet de pallier le manque de régularité. On obtient en effet, pour la norme H1, une convergence optimale des branches de solutions approchées vers les branches de solutions exactes
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Eslick, John. "A Dynamical Study of the Evolution of Pressure Waves Propagating through a Semi-Infinite Region of Homogeneous Gas Combustion Subject to a Time-Harmonic Signal at the Boundary." ScholarWorks@UNO, 2011. http://scholarworks.uno.edu/td/1367.
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In this dissertation, the evolution of a pressure wave driven by a harmonic signal on the boundary during gas combustion is studied. The problem is modeled by a nonlinear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for any transient effects to have dissipated. The zeroth, first and second-order perturbation solutions are obtained and their moduli are plotted against frequency. It is seen that the first and second-order corrections have unique maxima that shift to the right as the frequency decreases and to the left as the frequency increases. Dispersion relations are determined and their limiting behavior investigated in the low and high frequency regimes. It is seen that for low frequencies, the medium assumes a diffusive-like nature. However, for high frequencies the medium behaves similarly to one exhibiting relaxation. The phase speed is determined and its limiting behavior examined. For low frequencies, the phase speed is approximately equal to sqrt[ω/(n+1)] and for high frequencies, it behaves as 1/(n+1), where n is the mode number. Additionally, a maximum allowable value of the perturbation parameter, ε = 0.8, is determined that ensures boundedness of the solution. The location of the peak of the first-order correction, xmax, as a function of frequency is determined and is seen to approach the limiting value of 0.828/sqrt(ω) as the frequency tends to zero and the constant value of 2 ln 2 as the frequency tends to infinity. Analytic expressions are obtained for the approximate general perturbation solution in the low and high-frequency regimes and are plotted together with the perturbation solution in the corresponding frequency regimes, where the agreement is seen to be excellent. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from the boundary will be negligible. The perturbation solution and the finite-difference solution are found to be in excellent agreement. Thus, the validity of the perturbation method is established.
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Nascimento, Wanderley Nunes do. "Klein-Gordon models with non-effective time-dependent potential." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7453.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.
Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.
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Mtiraoui, Ahmed. "I. Etude des EDDSRs surlinéaires II. Contrôle des EDSPRs couplées." Thesis, Toulon, 2016. http://www.theses.fr/2016TOUL0010/document.
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Cette thèse aborde deux sujets de recherches, le premier est sur l’existence et l’unicité des solutions des Équations Différentielles Doublement Stochastiques Rétrogrades (EDDSRs) et les Équations aux Dérivées partielles Stochastiques (EDPSs) multidimensionnelles à croissance surlinéaire. Le deuxième établit l’existence d’un contrôle optimal strict pour un système controlé dirigé par des équations différentielles stochastiques progressives rétrogrades (EDSPRs) couplées dans deux cas de diffusions dégénérée et non dégénérée.• Existence et unicité des solutions des EDDSRs multidimensionnels :Nous considérons EDDSR avec un générateur de croissance surlinéaire et une donnée terminale de carré intégrable. Nous introduisons une nouvelle condition locale sur le générateur et nous montrons qu’elle assure l’existence, l’unicité et la stabilité des solutions. Même si notre intérêt porte sur le cas multidimensionnel, notre résultat est également nouveau en dimension un. Comme application, nous établissons l’existence et l’unicité des solutions des EDPS semi-linéaires.• Contrôle des EDSPR couplées :Nous étudions un problème de contrôle avec une fonctionnelle coût non linéaire dont le système contrôlé est dirigé par une EDSPR couplée. L’objective de ce travail est d’établir l’existence d’un contrôle optimal dans la classe des contrôle stricts, donc on montre que ce contrôle vérifie notre équation et qu’il minimise la fonctionnelle coût. La méthode consiste à approcher notre système par une suite de systèmes réguliers et on montre la convergence. En passant à la limite, sous des hypothèses de convexité, on obtient l’existence d’un contrôle optimal strict. on suit cette méthode théorique pour deux cas différents de diffusions dégénérée et non dégénéréeIn this Phd thesis, we considers two parts. The first one establish the existence and the uniquness of the solutions of multidimensional backward doubly stochastic differential equations (BDSDEs in short) and the stochastic partial differential equations (SPDEs in short) in the superlinear growth generators. In the second part, we study the stochastic controls problems driven by a coupled Forward-Backward stochastic differentialequations (FBSDEs in short).• BDSDEs and SPDEs with a superlinear growth generators :We deal with multidimensional BDSDE with a superlinear growth generator and a square integrable terminal datum. We introduce new local conditions on the generator then we show that they ensure the existence and uniqueness as well as the stability of solutions. Our work go beyond the previous results on the subject. Although we are focused on multidimensional case, the uniqueness result we establish is new in one dimensional too. As application, we establish the existence and uniqueness of probabilistic solutions tosome semilinear SPDEs with superlinear growth generator. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.• Controlled coupled FBSDEs :We establish the existence of an optimal control for a system driven by a coupled FBDSE. The cost functional is defined as the initial value of the backward component of the solution. We construct a sequence of approximating controlled systems, for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we get the existence of a feedback optimal control. The convexity condition is used to ensure that the optimal control is strict. In this part, we study two cases of diffusions : degenerate and non-degenerate
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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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Davidson, Bryan Duncan. "Recursive projection for semi-linear partial differential equations." Thesis, University of Bristol, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294932.
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El, Khomssi Mohammed. "Étude des équations paraboliques et elliptiques gérant l'état thermique d'un supraconducteur." Vandoeuvre-les-Nancy, INPL, 1994. http://www.theses.fr/1994INPL107N.
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L'état thermique d'un supraconducteur unidimensionnel est géré par une équation parabolique semi-linéaire ; le terme source représente ici la compétition entre la puissance volumique dissipée dans le conducteur par effet joule et celle qui est absorbée par le bain cryogénique de température Tb dont le rôle est de maintenir l'installation en dessous de sa température critique Tc. Après une perturbation thermique accidentelle (pendant laquelle seules les extrémités du conducteur peuvent être strictement contrôlées par le bain), la température du conducteur évolue de façon transitoire vers l'une des trois solutions stationnaires éventuellement possibles, parmi lesquelles T = Tb est la seule souhaitable. Ce mémoire propose: un certain nombre de critères suffisants, portant sur des paramètres physiques de l'installation, pour que T = Tb soit la seule solution stationnaire possible du problème ; une explicitation numérique d'un critère optimal (parce que nécessaire et suffisant) proposé dans une thèse antérieure mais peu exploitable sous sa forme théorique ; un calcul numérique des deux solutions stationnaires autres que Tb ; lorsque aucun des critères proposés ne peut être satisfait ; quelques informations sur l'évolution de la température après une perturbation thermique ; plusieurs généralisations de l'étude: situation tridimensionnelle, coefficient dépendant de la température, forme du terme source
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Blöthner, Florian [Verfasser]. "Non-Uniform Semi-Discretization of Linear Stochastic Partial Differential Equations in R / Florian Blöthner." München : Verlag Dr. Hut, 2019. http://d-nb.info/1181514207/34.
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Zhao, Huaizhong. "The stochastic elementary formula method and approximate travelling waves for semi-linear reaction diffusion equations." Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/4236/.
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In this thesis we consider approximate travelling wave solutions for stochastic and generalised KPP equations and systems by using the stochastic elementary formula method of Elworthy and Truman. We begin with the semi-classical analysis for generalised KPP equations. With a so-called "late caustic" assumption we prove that the global wave front is given by the Hamilton Jacobi function. We prove a Huygens principle on complete Riemannian manifolds without cut locus, with some bounds on their volume elements, in particular Cartan-Hadamard manifolds. Based on the semiclassical analysis we then consider the propagation of approximate travelling waves for stochastic generalised KPP equations. Three regimes of perturbation are considered: weak, mild, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to decay rapidly. In the more difficult mild case we show the existence of a 'wave front', in front of which the solution is close to zero (of order exp(-c1μ-2) as μ~0 for c1 random) and behind which it has at least order exp(-c2μ-1) for some random c2 depending on the increment of the noise. For an alternative stochastic equation we classify the effect of the noise by the Lyapunov exponent of a corresponding stochastic ODE. Finally we study the asymptotic behaviour of reaction-diffusion systems with a small parameter by using the n-dimensional Feynman-Kac formula and Freidlin's large deviation theory. We obtain the travelling wave with nonlinear ergodic interactions and a special case with nonlinear reducible interactions.
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Meyer, John Christopher. "Theoretical aspects of the Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4222/.
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The aim of this thesis is to provide a generic approach to the study of semi-linear parabolic partial differential equations when the nonlinearity fails to be Lipschitz continuous, but is in the class of Hӧlder continuous functions or the class of upper Lipschitz continuous functions. New results are obtained concerning the well-posedness (in the sense of Hadamard) of the initial value problem, namely, uniqueness and conditional continuous dependence results for upper Lipschitz continuous nonlinearities, and an existence result for Hӧlder continuous nonlinearities. To obtain these results, two new maximum principles have been obtained, for which examples have been provided to exhibit their applications and limitations. Additionally, new derivative estimates of Schauder-type have been obtained. Once the general theory has been established, specific problems are studied in detail. These show how one can apply the general theory, as well as problem specific approaches, to obtain well-posedness results.
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Chow, Tanya L. M., of Western Sydney Macarthur University, and Faculty of Business and Technology. "Systems of partial differential equations and group methods." THESIS_FBT_XXX_Chow_T.xml, 1996. http://handle.uws.edu.au:8081/1959.7/43.
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This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplishedFaculty of Business and Technology
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Pinheiro, Lucélia Kowalski. "EQUAÇÕES DIFERENCIAIS LINEARES SEM SOLUÇÃO." Universidade Federal de Santa Maria, 2014. http://repositorio.ufsm.br/handle/1/9987.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorIn this work we present the proof of a result due to Lars Hörmander which establishes a necessary condition for a linear operator with variable coefficients is globally resolvable.
Nesse trabalho apresentaremos a demonstração de um resultado devido à Lars Hörmander, que estabelece uma condição necessária para que um operador linear com coeficientes variáveis seja globalmente resolúvel.
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Dao, Tuan Anh. "Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales." TU Bergakademie Freiberg, 2020. https://tubaf.qucosa.de/id/qucosa%3A71649.
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The main goal of this thesis is to prove the global (in time) existence of small data Sobolev solutions to semi-linear damped σ-evolution equations from suitable function spaces basing on L^q spaces by mixing additional L^m regularity for the data on the basis of L^q-L^q estimates for solutions, with q∈(1,∞) and m∈[1,q), to the corresponding linear models. To establish desired results, we would like to apply the theory of modified Bessel functions, Faà di Bruno's formula and Mikhlin-Hörmander multiplier theorem in the treatment of linear problems. In addition, some of modern tools from Harmonic Analysis play a fundamental role to investigate results for the global existence of small data Sobolev solutions to semi-linear problems. Finally, the application of a modified test function method is to devote to the proof of blow-up results for semi-linear damped σ-evolution models, where σ≥1 and δ∈[0,σ) are assumed to be any fractional numbers.
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Naceur, Nahed. "Une méthode de décomposition de domaine pour la résolution numérique d’une équation non-linéaire." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0149.
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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
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Liu, Xuan. "Some contribution to analysis and stochastic analysis." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:485474c0-2501-4ef0-a0bc-492e5c6c9d62.
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The dissertation consists of two parts. The first part (Chapter 1 to 4) is on some contributions to the development of a non-linear analysis on the quintessential fractal set Sierpinski gasket and its probabilistic interpretation. The second part (Chapter 5) is on the asymptotic tail decays for suprema of stochastic processes satisfying certain conditional increment controls. Chapters 1, 2 and 3 are devoted to the establishment of a theory of backward problems for non-linear stochastic differential equations on the gasket, and to derive a probabilistic representation to some parabolic type partial differential equations on the gasket. In Chapter 2, using the theory of Markov processes, we derive the existence and uniqueness of solutions to backward stochastic differential equations driven by Brownian motion on the Sierpinski gasket, for which the major technical difficulty is the exponential integrability of quadratic processes of martingale additive functionals. A Feynman-Kac type representation is obtained as an application. In Chapter 3, we study the stochastic optimal control problems for which the system uncertainties come from Brownian motion on the gasket, and derive a stochastic maximum principle. It turns out that the necessary condition for optimal control problems on the gasket consists of two equations, in contrast to the classical result on ℝd, where the necessary condition is given by a single equation. The materials in Chapter 2 are based on a joint work with Zhongmin Qian (referenced in Chapter 2). Chapter 4 is devoted to the analytic study of some parabolic PDEs on the gasket. Using a new type of Sobolev inequality which involves singular measures developed in Section 4.2, we establish the existence and uniqueness of solutions to these PDEs, and derive the space-time regularity for solutions. As an interesting application of the results in Chapter 4 and the probabilistic representation developed in Chapter 2, we further study Burgers equations on the gasket, to which the space-time regularity for solutions is deduced. The materials in Chapter 4 are based on a joint work with Zhongmin Qian (referenced in Chapter 4). In Chapter 5, we consider a class of continuous stochastic processes which satisfy the conditional increment control condition. Typical examples include continuous martingales, fractional Brownian motions, and diffusions governed by SDEs. For such processes, we establish a Doob type maximal inequality. Under additional assumptions on the tail decays of their marginal distributions, we derive an estimate for the tail decay of the suprema (Theorem 5.3.2), which states that the suprema decays in a manner similar to the margins of the processes. In Section 5.4, as an application of Theorem 5.3.2, we derive the existence of strong solutions to a class of SDEs. The materials in this chapter is based on the work [44] by the author (Section 5.2 and Section 5.3) and an ongoing joint project with Guangyu Xi (Section 5.4).
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Dumas, Eric. "Un peu d'optique diffractive non-lineaire a phases courbes." Phd thesis, Université Rennes 1, 2000. http://tel.archives-ouvertes.fr/tel-00002525.
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On présente dans cette thèse quelques résultats nouveaux concernant l'optique non-linéaire diffractive. Tout d'abord, des solutions oscillantes régulières de systèmes hyperboliques sont analysées grâce à des développements asymptotiques (BKW) 3 échelles multiphases, à phases courbes : l'échelle la plus rapide est celle des oscillations, l'échelle intermédiaire décrit des phénomènes transverses à la propagation, cette dernière suivant les rayons de l'optique géométrique, à l'échelle la plus lente. L'utilisation des phases non planes permet de traiter le cas des systèmes à coefficients variables, et nécessite des hypothèses de cohérence et de petits diviseurs, dont on montre la généricité. On donne des exemples d'interactions d'ondes diffractées, en particulier en acoustique non linéaire. De plus, la diffraction transverse est considérée dans des cadres fonctionnels différents : périodique, faiblement décroissant, et pour des profils de chocs. Ces comportements sont appliqués à l'étude de la perturbation des phases oscillantes, ainsi qu'au problème des frontières ombre/lumière. On analyse dans chaque cas l'influence des effets de rectification (interaction entre moyenne et oscillations). Enfin, on décrit les oscillations se réfléchissant près d'un point diffractif (où la réflexion est tangentielle), pour une équation de Klein-Gordon semi-linéaire dissipative : une asymptotique $H^1$ met en évidence les interactions et la formation d'une \begin{guillemets}zone d'ombre\end{guillemets}.
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Aguiar, Ademir Alves. "Análise semi-local do método de Gauss-Newton sob uma condição majorante." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4251.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this dissertation we present a semi-local convergence analysis for the Gauss-Newton method to solve a special class of systems of non-linear equations, under the hypothesis that the derivative of the non-linear operator satisfies a majorant condition. The proofs and conditions of convergence presented in this work are simplified by using a simple majorant condition. Another tool of demonstration that simplifies our study is to identify regions where the iteration of Gauss-Newton is “well-defined”. Moreover, special cases of the general theory are presented as applications.
Nesta dissertação apresentamos uma análise de convergência semi-local do método de Gauss-Newton para resolver uma classe especial de sistemas de equações não-lineares, sob a hipótese que a derivada do operador não-linear satisfaz uma condição majorante. As demonstrações e condições de convergência apresentadas neste trabalho são simplificadas pelo uso de uma simples condição majorante. Outra ferramenta de demonstração que simplifica o nosso estudo é a identificação de regiões onde a iteração de Gauss-Newton está “bem-definida”. Além disso, casos especiais da teoria geral são apresentados como aplicações.
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Ibaouene, Youcef. "Processus Weyl presque périodique et équations différentielles stochastiques." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMR120.
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La thèse est dédiée à l'étude de certaines équations différentielles à coefficients Weyl presque périodiques. Elle contient deux parties essentielles : La première partie est consacrée à des problèmes déterministes. On y étudie l'existence et l'unicité d'une solution mild bornée Weyl presque périodique pour l'équation différentielle linéaire abstraite u’ (t) = Au(t) + f(t); t ∈ R; dans un espace de Banach X, où A : D(A) ⊂ X → X est un opérateur linéaire (non borné) qui génère un C0-semi-groupe exponentiellement stable et f : R → X est une fonction Weyl presque périodique. Finalement, toujours dans la première partie, nous étudions l'existence et l'unicité d'une solution mild bornée Weyl presque périodique pour l'équation différentielle semi-linéaire abstraite u’ (t) = Au(t) + f(t; u(t)); t ∈ R; où f : R x X, R → X est une fonction Weyl presque périodique en t ∈ R uniformément par rapport aux compacts de X. Dans la deuxième partie, nous généralisons ces études au cas stochastique. Précisément, nous étudions l'existence et l'unicité de solution Weyl presque périodique en loi pour une classe d'équations différentielles stochastiques semi-linéaires, dans un espace de Hilbert séparableThe thesis deals essentialy with a class of abstract dfferential equations with Weyl almost periodic coefficients, and comprises two part. The first part is devoted to the deterministic problems, in a first step, we study the existence and uniqueness of bounded Weyl almost periodic solution to the linear abstract differential equation u’ (t) = Au(t) + f(t); t ∈ R; in a Banach space X, where A : D(A) ⊂ X → X is a linear (unbounded) operator which generates an exponentially stable C0-semigroup on X and f : R → X is a Weyl almost periodic function. Finally, in a second step, always in the same frame, we consider the semi-linear differential equation u’ (t) = Au(t) + f(t; u(t)); t ∈ R ; where f(t; u) is a Weyl almost periodic in t ∈ R; uniformly with respect compact subsets of X. The second part, is concerned with the stochastic case. Precisely, we examine the existence and uniqueness of Weyl almost periodic solution in law to the abstract semilinear stochastic evolution equation on a Hilbert separable space
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Dao, Tuan Anh [Verfasser], Michael [Gutachter] Reissig, Michael [Akademischer Betreuer] Reissig, Marcelo [Gutachter] Ebert, and Rainer [Gutachter] Picard. "Global in time existence of Sobolev solutions to semi-linear damped sigma-evolution equations in L^q scales / Tuan Anh Dao ; Gutachter: Michael Reissig, Marcelo Ebert, Rainer Picard ; Betreuer: Michael Reissig." Freiberg : TU Bergakademie Freiberg, 2020. http://d-nb.info/1220779717/34.
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Edington, Joy Lynn. "Investigating the Stability of Bootstrapped Confirmatory Factor Analysis Estimates for Multiple Dimensions of the 2010 National Youth Nutrition and Physical Activity Study using Linear Structural Relations (LISREL)." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343847941.
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Yu, Haofeng. "A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29095.
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This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space.
The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions.Ph. D.
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Schulz, Julhane Alice Thomas. "Simulação numérica do escoamento bifásico em meios porosos heterogêneos empregando uma formulação semi-implícita, imitadores de fluxo e o método dos volumes finitos." Universidade do Estado do Rio de Janeiro, 2009. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=1240.
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Neste trabalho apresentamos um esquema numérico para a simulação computacional de escoamentos bifásicos, água-óleo, em reservatórios de petróleo. O modelo matemático consiste em um sistema de equações diferenciais parciais não-linear nas incógnitas velocidade, pressão e saturação. Uma quebra de operadores a dois níveis possibilita uma maior eficiência ao método permitindo que a velocidade, fornecida pelo problema de velocidade-pressão, seja atualizada somente para determinados intervalos de tempo associados ao problema de transporte advectivo-difusivo em termos da saturação. O método dos volumes finitos é empregado na resolução numérica do problema de velocidade-pressão e do transporte de massa por advecção e difusão. Na solução do problema de transporte de massa utilizamos limitadores de fluxo na aproximação dos termos advectivos e diferenças centradas para os termos difusivos. O nosso simulador foi validado a partir de confrontações dos seus resultados com as soluções teóricas conhecidas para os problemas unidimensionais, equações de Burgers e de Buckley-Leverett, e com outros resultados numéricos em se tratando do escoamento bifásico água-óleo bidimensional em meios porosos heterogêneos.A new numerical method is proposed for the solution of two-phase flow problem in petroleum reservoirs. The two-phase (water and oil) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. For computational eficiency an operator spliting technique is used; distinct time steps can be used for the computation of transport and pressure-velocity problems. The finite volume method is used in the numerical solution of the velocity-pressure and mass transport problems. A flux limiter is used for the numerical discretization of the advective terms while centered schemes are employed for the diffusion terms in the mass transport problem. In the validation of our numerical method we compared numerical and theoretical solutions for one dimensional problems, Burgers and Buckley-Leverett equations, and compared our numerical results to others, in the case of oil-water flows in two dimensions for an heterogeneous porous media.
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Pace, Michele. "Stochastic models and methods for multi-object tracking." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651396.
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La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.
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Chen, Ke-Ming, and 陳克鳴. "On the Numerical Blow-up Set for the Semi-linear Heat Equation." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/86620925437710064503.
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碩士國立中正大學
應用數學研究所
99
We consider the semi-linear parabolic blow-up problem u_t=u_{xx}+f(u) (0
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FANG, YONG-FU, and 方永富. "On the existence of positive solution of a semi-linear elliptic equation in Rn." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/96836506811198324985.
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Bui, Tang Bao Ngoc. "Semi-linear waves with time-dependent speed and dissipation." Doctoral thesis, 2013. https://tubaf.qucosa.de/id/qucosa%3A22925.
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The main goal of our thesis is to understand qualitative properties of solutions to the Cauchy problem for the semi-linear wave model with time-dependent speed and dissipation. We greatly benefited from very precise estimates for the corresponding linear problem in order to obtain the global existence (in time) of small data solutions. This reason motivated us to introduce very carefully a complete description for classification of our models: scattering, non-effective, effective, over-damping. We have considered those separately.
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Hergenroeder, AJ. "Moment Matching and Modal Truncation for Linear Systems." Thesis, 2012. http://hdl.handle.net/1911/71657.
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While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme.
In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation.
The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.
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Shih, Yi-Wen, and 施逸文. "Existence and Multiplicity of Solutions for Semi-linear Elliptic Equations." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/18903138654509963764.
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博士國立交通大學
應用數學系
87
In part 1 we study the problem of symmetry-breaking of positive symmetric solutions of a semi-linear elliptic equation on finite cylinders with mixed type boundary conditions in two dimentions. Taking the length as a bifurcation parameter, we prove that there are asymmetric bifurcations at certain critical numbers, and obtain some global results. In part 2 we consider some semi-linear elliptic equations with asymptotic linear non-linearity and show the existence, uniqueness, and asymptotic behavior of these solutions.
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Wu, Zhi-Jie, and 吳智傑. "Gradient Estimates for System of Semi-linear Equations and Liouville Theorem." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/00443767841521881320.
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碩士國立臺灣大學
數學研究所
90
We generalize the results for a scalar equation by Modica to the case of a system of equations. It is shown that if a bounded entire solution U(x) of a system of semi-linear equations satisfies the gradient bound |\nabla U|^{2}\leq 2F(U) for all x\in \Bbb R^{n}, then the Liouville theorem holds. Also we show that the inequality above holds if $F(U)$ satisfies some suitable assumptions.
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LI, MING-JIA, and 李明嘉. "Positive radial solutions and nonradial bifurcation for semi-linear elliptic equations in annuli and balls." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/80644115468145217628.
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Kliner, Jiří. "Soustavy lineárních rovnic na základní škole - obtíže žáků a pohled učitelů." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-340939.
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The goal of the diploma thesis was to describe critical moments for solving systems of linear equations at the primary school. First, various methods of solving systems of two linear equations with two unknowns are summarized, the history of systems of linear equations is briefly outlined and the theme is described from the point of view of curricular documents. Based on the review of literature, the critical moments and types of mistake made by pupils are described. My own research used the mixed research strategy, where the main strategy was qualitative and the secondary strategy was quantitative. The research consisted of semi-structured interviews with four mathematics teachers, the preparation and realization of a questionnaire for primary school pupils and the creation, realization and analysis of a didactic test. The main results of the thesis consists of the description of the most frequent pupils' problems when solving systems of linear equations, the didactic analysis of textbooks and teachers' views of the topic and its teaching. Keywords: linear equations and their systems, pupils' problems, mistakes, semi-structured interviews, didactic test Powered by TCPDF (www.tcpdf.org)