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Dissertations / Theses on the topic 'Degenerate equation'

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Published: 9 March 2023
Last updated: 31 July 2025

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1

Tepoyan, L. "The mixed problem for a degenerate operator equation." Universität Potsdam, 2008. http://opus.kobv.de/ubp/volltexte/2009/3033/.

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We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.
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2

Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions in domains with Levi degenerate boundaries." [S.l.] : [s.n.], 2002. http://dochost.rz.hu-berlin.de/dissertationen/brinkschulte-judith-2002-04-19.

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3

Picard, Sebastien. "A priori estimates of the degenerate Monge-Ampère equation on compact Kähler manifolds." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119756.

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The regularity theory of the degenerate complex Monge-Ampère equation is studied. First, the equation is considered on a compact Kahler manifold without boundary. Accordingly, some background information on Kahler geometry is presented. Given a solution of the degenerate complex Monge-Ampère equation, it is shown that its oscillation and gradient can be bounded. The Laplacian of the solution is also estimated. There is a slight improvement from the literature on the conditions required in order to obtain the estimate on the Laplacian of the solution, however the estimates developed only hold i
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4

Brinkschulte, Judith. "The Cauchy-Riemann equation with support conditions on domains with Levi-degenerate boundaries." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14734.

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In einem ersten Teil betrachten wir ein relativ kompaktes Gebiet Omega einer n-dimensionalen Kähler-Mannigfaltigkeit, mit Lipschitz-Rand, welches eine gewisse "log delta"-Pseudokonvexität besitzt. Wir zeigen, dass die Cauchy-Riemann Gleichung mit exaktem Träger in Omega für alle Bigrade (p,q) mit 0< q< n-1 eine Lösung besitzt. Ausserdem ist das Bild des Cauchy-Riemann Operators auf glatten (p,n-1)-Formen mit exaktem Träger in Omega abgeschlossen. Wir geben Anwendungen für die Lösbarkeit der tangentialen Cauchy-Riemann Gleichungen für glatte Formen und Ströme auf Rändern von schwach pseudokonve
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5

Mattioli, Mauro. "Estimates on degenerate jump-diffusion processes and regularity of the related valuation equation." Doctoral thesis, Luiss Guido Carli, 2011. http://hdl.handle.net/11385/200886.

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Many risk-neutral pricing problems proposed in the finance literature require to be dealt with by solving the corresponding Partial Integro-Differential Equation. Unfortunately, neither the standard Sobolev spaces theory, or the present literature on viscosity solution theory is able to deal with some problems of interest in finance. A recent result presented by Costantini, Papi and D’Ippoliti accepted for pubblication on Finance and Stochastics [17], shows that, under general conditions on the coefficients of the stochastic integro-differential equation, whenever a Lyapunov-type condition is
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6

Watling, K. D. "Formulae for solutions to (possibly degenerate) diffusion equations exhibiting semi-classical and small time asymptotics." Thesis, University of Warwick, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380277.

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7

ROCCHETTI, DARIO. "Generation of analytic semigroups for a class of degenerate elliptic operators." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2009. http://hdl.handle.net/2108/749.

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Questa tesi è suddivisa in due capitoli. Nel primo si da un risultato di buona positura per una classe di problemi parabolici degeneri. I risultati ottenuti, validi in dimensione 2, garantiscono che le soluzioni di tali problemi supportano l'integrazione per parti. Nel secondo capitolo, si studia la controllabilità allo zero per una classe di operatori parabolici degeneri in forma non-divergenza. In particolare, i coefficienti del termine del secondo ordine possono degenerare al bordo del dominio spaziale. A questo scopo si giunge previo una disuguaglianza di osservabilità per il pro
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8

Rao, Arvind Satya. "Weak solutions to a Monge-Ampère type equation on Kähler surfaces." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/582.

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In the context of moment maps and diffeomorphisms of Kähler manifolds, Donaldson introduced a fully nonlinear Monge-Ampère type equation. Among the conjectures he made about this equation is that the existence of solutions is equivalent to a positivity condition on the initial data. Weinkove later affirmed Donaldson's conjecture using a gradient flow for the equation in the space of Kähler potentials of the initial data. The topic of this thesis is the case when the initial data is merely semipositive and the domain is a closed Kähler surface. Regularity techniques for degenerate Monge-Ampère
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9

URBANI, CRISTINA. "Bilinear Control of Evolution Equations." Doctoral thesis, Gran Sasso Science Institute, 2020. http://hdl.handle.net/20.500.12571/10061.

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The thesis is devoted to the study of the stabilization and the controllability of the evolution equations $$u'(t) + Au (t) + p (t) Bu (t) = 0$$ by means of a bilinear control $p$. Bilinear controls are coefficients of the equation that multiply the state variable. Multiplicative controls are therefore suitable to describe processes that change their principal parameters in presence of a control. We first present a result of rapid stabilization of the parabolic equations towards the ground state by bilinear control with a doubly exponential rate of convergence. Under stronger hypothese
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10

Boiger, Wolfgang Josef. "Stabilised finite element approximation for degenerate convex minimisation problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16790.

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Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätz
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11

Čakaitė, Inga. "Dalinių išvestinių sistemos su kvazireguliariuoju išsigimimu sprendimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2006. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2006~D_20060609_122917-49917.

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The system of the four partial fluxions of the primary row of differential equations the row of which dwindles at the points of plane has been analysed. The systems of the expressions of families of the detached solutions have been derived by converging degree rows at the environment of malformation rows through the technique of summation of degree rows. The solutions at the malformation points are particular for having degree particularities. Still, the particularities depend on the other to variables, in conformity to which there are no system malformation weigh. The effect is not evident in
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12

Mumcu, Gokhan. "EM Characterization of Magnetic Photonic / Degenerate Band Edge Crystals and Related Antenna Realizations." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1221860344.

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13

GOFFI, ALESSANDRO. "Topics in nonlinear PDEs: from Mean Field Games to problems modeled on Hörmander vector fields." Doctoral thesis, Gran Sasso Science Institute, 2019. http://hdl.handle.net/20.500.12571/9808.

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This thesis focuses on qualitative and quantitative aspects of some nonlinear PDEs arising in optimal control and differential games, ranging from regularity issues to maximum principles. More precisely, it is concerned with the analysis of some fully nonlinear second order degenerate PDEs over Hörmander vector fields that can be written in Hamilton-Jacobi-Bellman and Isaacs form and those arising in the recent theory of Mean Field Games, where the prototype model is described by a coupled system of PDEs involving a backward Hamilton-Jacobi and a forward Fokker-Planck equation. The thesis is d
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14

Civin, Damon. "Stability of charged rotating black holes for linear scalar perturbations." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247397.

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In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and
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15

Bredies, Kristian. "Optimal control of degenerate parabolic equations in image processing analysis of evolution equations with variable degeneracy and associated minimization problems." Berlin Logos-Verl, 2007. http://d-nb.info/987598511/04.

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16

Bredies, Kristian. "Optimal control of degenerate parabolic equations in image processing : analysis of evolution equations with variable degeneracy and associated minimization problems /." Berlin : Logos-Verl, 2008. http://deposit.d-nb.de/cgi-bin/dokserv?id=3071675&prov=M&dok_var=1&dok_ext=htm.

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17

Moyano, Garcia Iván. "Controllability of of some kinetic equations, of parabolic degenerated equations and of the Schrödinger equation via domain transformation." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX062/document.

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Ce mémoire présente les travaux réalisés au cours de ma thèse dans le but d'étudier la contrôlabilité de quelques équations aux dérivées partielles. La première partie de cette thèse est consacrée à l'étude de la contrôlabilité de quelques équations cinétiques en différents régimes. Dans un régime collisionnel, nous étudions la contrôlabilité de l'équation de Kolmogorov, un modèle de type Fokker-Planck cinétique, posée dans l'espace de phases $R^d times R^d$. Nous obtenons la contrôlabilité à zéro de cette équation grâce à l'utilisation d'une inégalité spectrale associée à l'opérateur Laplacie
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18

Figalli, Alessio. "Optimal transportation and action-minimizing measures." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85683.

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19

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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20

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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21

MARINO, LORENZO. "Regolarizzazione debole attraverso rumore di Lévy degenere e sue applicazioni." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2021. http://hdl.handle.net/10281/330542.

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Dopo un'introduzione generale sul fenomeno della regolarizzazione attraverso rumore in un contesto degenere, la prima parte di questa tesi si concentra nello stabilire le stime di Schauder, un strumento analitico utile per dimostrare anche il carattere ben posto di equazioni differenziali stocastiche (EDS), per due classi di equazioni di Kolmogorov sotto una condizione di tipo Hörmander debole, i cui coefficienti giacciono in opportuni spazi di Hölder anisotropi con multi-indici di regolarità. La prima classe considera un sistema non lineare controllato da un operatore simmetrico ⍺-stabile che
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22

Zhang, Zhou Ph D. Massachusetts Institute of Technology. "Degenerate Monge-Ampere equations over projective manifolds." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34685.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (p. 253-257).<br>In this thesis, we study degenerate Monge-Ampere equations over projective manifolds. The main degeneration is on the cohomology class which is Kähler in classic cases. Our main results concern the case when this class is semi-ample and big with certain generalization to more general cases. Two kinds of argum
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23

Tepoyan, Liparit. "Degenerated operator equations of higher order." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2588/.

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24

Pereira, Liliana Angélica Costa Matos. "Approximation of degenerate partial differential equations arising in finance." Doctoral thesis, Instituto Superior de Economia e Gestão, 2018. http://hdl.handle.net/10400.5/15849.

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Doutoramento em Matemática Aplicada à Economia e Gestão<br>Esta dissertação estuda a discretização de equações diferenciais parciais degeneradas com aplicações às Finanças. Em particular, o problema de Cauchy para uma equação diferencial parcial linear de segunda ordem é discretizado nas variáveis espaciais para os casos de coeficientes limitados e ilimitados. A semi-discretização é considerada para a versão multidimensional da EDP e também para o caso particular de uma dimensão espacial. A aproximação à solução da EDP é obtida com recurso a métodos básicos de diferenças finitas em v
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25

Zhan, Yi. "Viscosity solutions of nonlinear degenerate parabolic equations and several applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49931.pdf.

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26

Pang, Ho Cheung. "Analysis on stochastic anisotropic degenerate parabolic-hyperbolic mixed-type equations." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4364a7ef-07fa-458a-bd59-3de79f092144.

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This dissertation consists chiefly of three parts, which tell different facets in the development of one topic. The first part is an exploration of continuous dependence estimates of stochastically driven degenerate parabolic equations. The second is an extension of work done by Debussche and Vovelle on first order stochastic conservation laws - we extend their results to degenerate parabolic-hyperbolic conservation laws with additive noise, and derive results on the existence and uniqueness of invariant measures. In the third part we explore the long time behaviour of solutions to stochastic
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27

Maizurna, Isna. "Semigroup methods for degenerate cauchy problems and stochastic evolution equations /." Title page, abstract and contents only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09phm2328.pdf.

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28

Voldman, Aleksandr. "Topological classification of non-degenerate quadratic system." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1192.

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29

Götmark, Elin, and Kaj Nyström. "Boundary behaviour of non-negative solutions to degenerate sub-elliptic equations." Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-164532.

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Let X = {X-1, ..., X-m} be a system of C-infinity vector fields in R-n satisfying Hormander's finite rank condition and let Omega be a non-tangentially accessible domain with respect to the Carnot-Caratheodory distance d induced by X. We study the boundary behavior of non-negative solutions to the equation Lu = Sigma(i, j -1) X-i*(a(ij)X(j)u) = Sigma X-i, j=1(i)*(x)(aij(x)X-j(x)u(x)) = 0 for some constant beta &gt;= 1 and for some non-negative and real-valued function lambda = lambda(x). Concerning kappa we assume that lambda defines an A(2)-weight with respect to the metric introduced by the
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30

Schneider, Mathias. "Finite element approximation of some degenerate/singular elliptic and parabolic equations." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265861.

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31

Sánchez, Garduño Faustino. "Travelling waves in one-dimensional degenerate non-linear reaction-diffussion equations." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334929.

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32

Agueh, Martial Marie-Paul. "Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/29180.

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33

Abedin, Farhan. "Harnack Inequality for a class of Degenerate Elliptic Equations in Non-Divergence Form." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/523174.

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Mathematics<br>Ph.D.<br>We provide two proofs of an invariant Harnack inequality in small balls for a class of second order elliptic operators in non-divergence form, structured on Heisenberg vector fields. We assume that the coefficient matrix is uniformly positive definite, continuous, and symplectic. The first proof emulates a method of E. M. Landis, and is based on the so-called growth lemma, which establishes a quantitative decay of oscillation for subsolutions. The second proof consists in establishing a critical density property for non-negative supersolutions, and then invoking the axi
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34

CIBELLI, Gennaro. "Sharp Estimates for Fundamental Solutions of some degenerate Kolmogorov equations arising in Finance." Doctoral thesis, Università degli studi di Ferrara, 2017. http://hdl.handle.net/11392/2488066.

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The thesis is devoted to the study of a degenerate parabolic partial differential equation which arises in models for the pricing of Arithmetic Average Asian Options in Finance in the framework introduced by Black, Scholes and Merton. The aim of the work is to prove optimal estimates for the fundamental solution of the related operator. The interest in this result is in that an expression of the fundamental solution is not available, whereas explicit information on its asymptotic behaviour are provided in the work. The problem of proving upper and lower estimates for the fundamental solutio
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35

Iwaki, Kohei. "On WKB theoretic transformations for Painleve transcendents on degenerate Stokes segments." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188457.

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36

Pesce, Antonello. "Stochastic fundamental solutions for a class of degenerate SPDEs." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14559/.

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In this thesis, we look for a fundamental solution for a broad, possibly degenerate class of stochastic partial differential equations (SPDEs), whose deterministic part is a Kolmogorov equation with coefficients measurable in the time variable. We use a version of the It\^o-Wentzell formula to reduce the SPDE to a PDE, for which we extend the classic Levi's parametrix method to find a fundamental solution.
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37

Chen, Hua, and Ke Li. "The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3024/.

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Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.
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38

Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.

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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the met
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39

Figalli, Alessio. "Optimal transportation and action-minimizing measures." Doctoral thesis, Lyon, École normale supérieure (sciences), 2007. http://www.theses.fr/2007ENSL0422.

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40

Lucertini, Giacomo. "Parametrix technique for a class of degenerate parabolic operators with measurable coefficients under the weak Hörmander condition." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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In this thesis we study a wide class of differential operators of Kolmogorov type characterized by two structural hypotheses: it is satisfied the weak Hörmander condition and the coefficients are merely measurable in time variable. The main purpose of this work is to adapt the classical Levi parametrix method to this framework, in order to construct a fundamental solution of the operator. In particular, we will use a time-dependent parametrix. This problem is strongly related to the study of stochastic differential equations (SDEs), since the backward Kolmogorov operators associated to some
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41

MORALES, DANIA GONZALEZ. "TWO TOPICS IN DEGENERATE ELLIPTIC EQUATIONS INVOLVING A GRADIENT TERM: EXISTENCE OF SOLUTIONS AND A PRIORI ESTIMATES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36440@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>Esta tese tem o intuito do estudo da existência, não existência e estimativas a priori de soluções não negativas de alguns tipos de problemas elípticos degenerados coercivos e não coercivos com um termo adicional dependendo do gradiente. Dentre outras coisas, obtemos condições integrais generalizadas tipo Keller-Osserman para a existência e não existência de soluções. Também mostramos
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42

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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43

Tarhini, Rana. "Équation de films minces fractionnaire pour les fractures hydrauliques." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1061/document.

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Ces travaux concernent deux équations paraboliques, dégénérées et non-locales. La première équation est une équation de films minces fractionnaire et la deuxième est une équation des milieux poreux fractionnaire. La présentation des problèmes, les résultats existants dans la littérature, ainsi que le résumé de nos résultats font l'objet de l'introduction. Le deuxième chapitre est consacré à la présentation de la méthode de De Giorgi utilisée pour montrer la régularité Hölder des solutions des équations elliptiques. On présente de plus les résultats utilisant cette approche dans les cas parabol
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44

Tamekue, Cyprien. "Controllability, Visual Illusions and Perception." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPAST105.

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Cette thèse explore deux applications distinctes de la théorie du contrôle dans différents domaines scientifiques : la physique et les neurosciences. La première application se concentre sur la contrôlabilité nulle de l'équation parabolique associée à l'opérateur de Baouendi-Grushin sur la sphère de dimension 2. En revanche, la deuxième application concerne la description mathématique des illusions visuelles du type MacKay, et se focalise sur l'effet MacKay et les expériences psychophysiques de Billock et Tsou, via le contrôle de l'équation des champs neuronaux à une seule couche du type Amari
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Krüger, Matthias [Verfasser], Ingo [Akademischer Betreuer] Witt, Ingo [Gutachter] Witt, and Dorothea [Gutachter] Bahns. "On the Cauchy problem for a class of degenerate hyperbolic equations / Matthias Krüger ; Gutachter: Ingo Witt, Dorothea Bahns ; Betreuer: Ingo Witt." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2018. http://d-nb.info/1166399818/34.

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46

Leobacher, Gunther, and Michaela Szölgyenyi. "Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient." Springer Nature, 2018. http://dx.doi.org/10.1007/s00211-017-0903-9.

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We prove strong convergence of order 1/4 - E for arbitrarily small E > 0 of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying the Euler-Maruyama scheme to a transformation of the SDE we aim to solve.
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47

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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48

De, Zan Cecilia. "Some new results on reaction-diffusion equations and geometric flows." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422529.

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In this thesis we discuss the asymptotic behavior of the solutions of scaled reaction-diffusion equations in the unbounded domain Rn × (0 + ∞), in the cases when such a behavior is described in terms of moving interfaces. As first class of asymptotic problems we consider the singular limit of bistable reaction-diffusion equations in the case when the velocity of the traveling wave equation depends on the space variable, i.e. cε = cε(x), and it satisfies, in some suitable sense, cε/ετ → α, as ε → 0+, where α is a discontinuous function and τ is an integer that can be equal to 0 or 1. The secon
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49

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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Leahy, James-Michael. "On parabolic stochastic integro-differential equations : existence, regularity and numerics." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.

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In this thesis, we study the existence, uniqueness, and regularity of systems of degenerate linear stochastic integro-differential equations (SIDEs) of parabolic type with adapted coefficients in the whole space. We also investigate explicit and implicit finite difference schemes for SIDEs with non-degenerate diffusion. The class of equations we consider arise in non-linear filtering of semimartingales with jumps. In Chapter 2, we derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by Lévy driven stochastic differential equations (SDEs) with adap
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