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Dissertations / Theses on the topic 'Systems of Parabolic Equations'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Crooks, Elaine Craig Mackay. "Travelling-wave solutions for parabolic systems." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319218.

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2

Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is rev

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3

Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.<br>Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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4

Reichelt, Sina. "Two-scale homogenization of systems of nonlinear parabolic equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17385.

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Ziel dieser Arbeit ist es zwei verschiedene Klassen von Systemen nichtlinearer parabolischer Gleichungen zu homogenisieren, und zwar Reaktions-Diffusions-Systeme mit verschiedenen Diffusionslängenskalen und Gleichungen vom Typ Cahn-Hilliard. Wir betrachten parabolische Gleichungen mit periodischen Koeffizienten, wobei die Periode dem Verhältnis der charakteristischen mikroskopischen zu der makroskopische Längenskala entspricht. Unser Ziel ist es, effektive Gleichungen rigoros herzuleiten, um die betrachteten Systeme besser zu verstehen und den Simulationsaufwand zu minimieren. Wir suchen a

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5

Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

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6

Floater, Michael S. "Blow-up of solutions to nonlinear parabolic equations and systems." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235037.

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7

Chen, Mingxiang. "Structural stability of periodic systems." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29341.

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8

Floridia, Giuseppe. "Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1051.

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This thesis consists of two parts, both related to the theory of parabolic equations and systems. The first part is devoted to control theory which studies the possibility of influencing the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology. In the second part of the thesis we address regularity issues on the local differentiability and H\"older regularity for weak solutions of nonlinear systems in divergence form.

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9

Al, Refai Mohammed. "Sequential eigenfunction expansion for certain non-linear parabolic systems and wave type equations." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36747.

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In trying to solve nonlinear partial differential equations with time dependence using the Galerkin method, one ends up with solving nonlinear systems of ordinary differential equations, which are not easily solved. In this thesis we introduce a new iterative method based on eigenfunction expansion to deal with the finite non-linear systems sequentially.<br>We apply the new method to integrate the semi-linear parabolic equation ut=12u+fu ,x∈D with homogeneous Dirichlet or Robin boundary conditions. We prove the convergence of the new iterative method, and use it to find the multiple solut

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10

Zhao, Yaxi. "Numerical solutions of nonlinear parabolic problems using combined-block iterative methods /." Electronic version (PDF), 2003. http://dl.uncw.edu/etd/2003/zhaoy/yaxizhao.pdf.

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11

Cao, Yanzhao. "Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equations." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/37771.

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The exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exa

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12

ADDONA, DAVIDE. "Parabolic operators with unbounded coefficients with applications to stochastic optimal control games." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/76535.

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The aim of this thesis is to improve some results on parabolic Cauchy problems with unbounded coefficients and their connection with stochastic optimal games. In the first part we summarize the recent results on parabolic operators with unbounded coefficients and on stochastic optimal control problem. In particular, in the matter of analyitic results, we recall the main exstence and uniqueness theorems for parabolic Cauchy problems with unbounded coefficients, the gradient estimates for the associated evolution operator, and its continuity and compactness properties. About the stochastic part

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13

Moreno, Claudia. "Control of partial differential equations systems of dispersive type." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASV031.

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Il existe peu de résultats dans la littérature sur la contrôlabilité du système d'équations aux dérivées partielles. Dans cette thèse, nous considérons l'étude des propriétés de contrôle pour trois systèmes couplés d'équations aux dérivées partielles de type dispersif et un problème inverse de récupération d’un coefficient. Le premier système est formé par N équations de Korteweg-de Vries sur un réseau en forme d'étoile. Pour ce système, nous étudierons la contrôlabilité exacte avec N contrôles placés aux extrémités du réseau. Le deuxième système couple trois équations de Korteweg-de Vries. Ce

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14

Zelley, Christopher Andrew. "Radiowave propagation over irregular terrain using the parabolic equation method." Thesis, University of Birmingham, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390682.

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15

Reichelt, Sina [Verfasser], Alexander [Akademischer Betreuer] Mielke, Dorothee [Akademischer Betreuer] Knees, and Adrian [Akademischer Betreuer] Muntean. "Two-scale homogenization of systems of nonlinear parabolic equations / Sina Reichelt. Gutachter: Alexander Mielke ; Dorothee Knees ; Adrian Muntean." Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://d-nb.info/1080558411/34.

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16

Song, Yongcun. "An ADMM approach to the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/551.

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We address in this thesis the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations. For the unconstrained or control-constrained optimal control problem, the first order optimality condition can be obtained in a general way and the associated Lagrange multiplier has low regularity, such as in the L²(Ω). However, for state-constrained optimal control problems, additional assumptions are required in general to guarantee the existence and regularity of Lagrange multipliers. The resulting optimality system leads to difficulties for both

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17

Post, Katharina. "A System of Non-linear Partial Differential Equations Modeling Chemotaxis with Sensitivity Functions." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14365.

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Wir betrachten ein System nichtlinearer parabolischer partieller Differentialgleichungen zur Modellierung des biologischen Phänomens Chemotaxis, das unter anderem in Aggregationsprozessen in Lebenszyklen bestimmter Einzeller eine wichtige Rolle spielt. Unser Chemotaxismodell benutzt Sensitivitäts funktionen, die die vorkommenden biologischen Prozesse genauer spezifizieren. Trotz der durch die Sensitivitätsfunktionen eingebrachten, zusätzlichen Nichtlinearitäten in den Gleichungen erhalten wir zeitlich globale Existenz von Lösungen für verschiedene biologisch realistische Klassen von Sensitiv

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18

Rolland, Guillaume. "Global existence and fast-reaction limit in reaction-diffusion systems with cross effects." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00785757.

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This thesis is devoted to the study of parabolic systems of partial differential equations arising in mass action kinetics chemistry, population dynamics and electromigration theory. We are interested in the existence of global solutions, uniqueness of weak solutions, and in the fast-reaction limit in a reaction-diffusion system. In the first chapter, we study two cross-diffusion systems. We are first interested in a population dynamics model, where cross effects in the interactions between the different species are modeled by non-local operators. We prove the well-posedness of the correspondi

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19

Krainer, Thomas, and Bert-Wolfgang Schulze. "On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 1: Chapter 1+2]." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2598/.

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We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is sp

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20

Krainer, Thomas, and Bert-Wolfgang Schulze. "On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 2: Chapter 3-5]." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2599/.

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We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is sp

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21

Krainer, Thomas, and Bert-Wolfgang Schulze. "On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 3: Chapter 6+7]." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2600/.

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We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is sp

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22

Hill, Thomas Ian. "Complete Blow Up for Parabolic System Arising in a Theory of Thermal Explosion of Porous Energetic Materials." University of Akron / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1428939894.

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23

Le, Balc'h Kévin. "Contrôlabilité de systèmes de réaction-diffusion non linéaires." Thesis, Rennes, École normale supérieure, 2019. http://www.theses.fr/2019ENSR0016/document.

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Cette thèse est consacrée au contrôle de quelques équations aux dérivées partielles non linéaires. On s’intéresse notamment à des systèmes paraboliques de réaction-diffusion non linéaires issus de la cinétique chimique. L’objectif principal est de démontrer des résultats de contrôlabilité locale ou globale, en temps petit, ou en temps grand.Dans une première partie, on démontre un résultat de contrôlabilité locale à des états stationnaires positifs en temps petit, pour un système de réaction-diffusion non linéaire.Dans une deuxième partie, on résout une question de contrôlabilité globale à zér

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24

Rieger, Marc Oliver. "Nonconvex Dynamical Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37269.

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Many problems in continuum mechanics, especially in the theory of elastic materials, lead to nonlinear partial differential equations. The nonconvexity of their underlying energy potential is a challenge for mathematical analysis, since convexity plays an important role in the classical theories of existence and regularity. In the last years one main point of interest was to develop techniques to circumvent these difficulties. One approach was to use different notions of convexity like quasi-- or polyconvexity, but most of the work was done only for static (time independent) equations. In this

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25

Cauvin, vila Jean. "Cross-diffusion systems in moving-boundary domains." Electronic Thesis or Diss., Marne-la-vallée, ENPC, 2023. http://www.theses.fr/2023ENPC0050.

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Cette thèse traite de l’analyse, de la stabilisation et de l’approximation numérique de systèmes d’EDP à diffusion croisée dans des domaines à frontière mobile. Elle est motivée par la modélisation d’un processus de dépôt vapeur pour la synthèse de couches minces. Le travail original est divisé en trois parties. Un premier travail concerne la stabilisation d’un système à diffusion croisée dans un domaine unidimensionnel en expansion : considérant que l’on peut contrôler les données au bord du système, nous construisons via la méthode de backstepping une loi de rétro- action qui stabilise expon

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26

Pires, Leonardo. "Rate of convergence of attractors for abstract semilinear problems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27102016-090449/.

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In this work we study rate of convergence of attractors for parabolic equations. We consider various types of problems where the diffusion coefficient has varied profiles: large diffusion, localized large diffusion and large diffusion except in the neighborhood of a point where it becomes small. In all cases we obtain a singular perturbation where a rate of convergence of attractors is obtained.<br>Neste trabalho estudamos taxa de convergência de atratores para equações parabólicas. Consideramos vários tipos de problemas onde o coeficiente de difusão apresenta perfís variados: difusão grande,

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27

Li, Ji. "Analyse mathématique de modèles d'intrusion marine dans les aquifères côtiers." Thesis, Littoral, 2015. http://www.theses.fr/2015DUNK0378/document.

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Le thème de cette thèse est l'analyse mathématique de modèles décrivant l'intrusion saline dans les aquifères côtiers. On a choisi d'adopter la simplicité de l'approche avec interface nette : il n'y a pas de transfert de masse entre l'eau douce et l'eau salée (resp. entre la zone saturée et la zone sèche). On compense la difficulté mathématique liée à l'analyse des interfaces libres par un processus de moyennisation verticale nous permettant de réduire le problème initialement 3D à un système d'edps définies sur un domaine, Ω, 2D. Un second modèle est obtenu en combinant l'approche 'interface

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28

Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.

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In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse proble

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29

Sa, Ngiamsunthorn Parinya. "Domain perturbation for parabolic equations." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/7775.

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We study the effect of domain perturbation on the behaviour of parabolic equations. The first aspect considered in this thesis is the behaviour of solutions under changes of the domain. We show how solutions of linear and semilinear parabolic equations behave as a sequence of domains $\Omega_n$ converges to an open set $\Omega$ in a certain sense. In particular, we are interested in singular domain perturbations so that a change of variables is not possible on these domains. For autonomous linear equations, it is known that convergence of solutions under domain perturbation is closely related

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30

Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.

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The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow;

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31

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the s

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32

Dekkers, Sophia Antonia Janna. "Degenerate parabolic equations on Riemannanian manifolds." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405755.

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33

Parvin, S. "Diffusion-convection problems in parabolic equations." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382761.

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34

Ribeiro, Saraiva L. M. "Removable singularities and quasilinear parabolic equations." Thesis, University of Sussex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356520.

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35

Elbirki, Asma. "On parabolic equations with gradient terms." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/66012/.

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This thesis is concerned with the study of the important effect of the gradient term in parabolic problems. More precisely, we study the global existence or nonexistence of solutions, and their asymptotic behaviour in finite or infinite time. Particularly when the power of the gradient term can increase to the power function of the solution. This thesis consists of five parts. (i) Steady-State Solutions, (ii) The Blow-up Behaviour of the Positive Solutions, (iii) Parabolic Liouville-Type Theorems and the Universal Estimates, (iv) The Global Existence of the Positive Solutions, (v) Viscous Hami

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36

Pang, Huadong. "Parabolic equations without a minimum principle." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38958.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.<br>Includes bibliographical references (p. 63-64).<br>In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and existence of the solution for initial data, which may not be continuous at two boundary points. We also examine the circumstances when these solutions admit a probabilistic interpretation. Some partial results are given for analogous problems in

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37

Tsegmid, Munkhgerel. "Modélisation d’aquifères peu profonds en interaction avec les eaux de surfaces." Thesis, Littoral, 2019. http://www.theses.fr/2019DUNK0526/document.

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Nous présentons une classe de nouveaux modèles pour décrire les écoulements d’eau dans des aquifères peu profonds non confinés. Cette classe de modèles offre une alternative au modèle Richards 3d plus classique mais moins maniable. Leur dérivation est guidée par deux ambitions : le nouveau modèle doit d’une part être peu coûteux en temps de calcul et doit d’autre part donner des résultats pertinents à toute échelle de temps. Deux types d’écoulements dominants apparaissent dans ce contexte lorsque le rapport de l’épaisseur sur la longueur de l’aquifère est petit : le premier écoulement apparaît

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38

Fontana, Eleonora. "Maximum Principle for Elliptic and Parabolic Equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12061/.

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Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.

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39

Takayama, Yuuya. "Nahm’s equations, quiver varieties and parabolic sheaves." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/204570.

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40

Keras, Sigitas. "Numerical methods for parabolic partial differential equations." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/251611.

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41

Sande, Olow. "Boundary Estimates for Solutions to Parabolic Equations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-281451.

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This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of tw

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42

Sockell, Michael Elliot. "Similarity solutions of stochastic nonlinear parabolic equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49898.

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A novel statistical technique introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in terms of the moments of the wave function. In the latter, all even-order moments are computed exactly, whereas the odd-order moments are solved asymptotically. Lastly, it is shown that this statistical technique is isomorphic to mappi

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43

Petitta, Francesco. "Nonlinear parabolic equations with general measure data." Doctoral thesis, La Sapienza, 2006. http://hdl.handle.net/11573/917105.

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44

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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45

Ascencio, Pedro. "Adaptive observer design for parabolic partial differential equations." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/49454.

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This thesis addresses the observer design problem, for a class of linear one-dimensional parabolic Partial Differential Equations, considering the simultaneous estimation of states and parameters from boundary measurements. The design is based on the Backstepping methodology for Partial Differential Equations and extends its central idea, the Volterra transformation, to compensate for the parameters uncertainties. The design steps seek to reject time-varying parameter uncertainties setting forth a type of differential boundary value problems (Kernel-PDE/ODEs) to accomplish its objective, the s

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46

Yi, Zhuobiao. "Identification of General Source Terms in Parabolic Equations." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1036084593.

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47

Romutis, Todd. "Numerical Smoothness and Error Analysis for Parabolic Equations." Bowling Green State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1522150799203255.

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48

Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and A

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Williams, J. F. "Scaling and singularities in higher-order nonlinear differential equations." Thesis, University of Bath, 2003. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275878.

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Nam, Dukjin. "Multiscale numerical methods for some types of parabolic equations." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2993.

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