title: Nonlinear Pseudoparabolic Equations and Variational Inequalities
creator: Ptashnyk, Mariya
subject: 510
subject: 510 Mathematics
description: The aim of this thesis is to prove existence and uniqueness of weak solutions for some types of quasilinear and nonlinear pseudoparabolic equations and for some types of quasilinear and nonlinear  variational inequalities. The pseudoparabolic equations are characterized by the presence of mixed third order derivatives. Here the existence theory for degenerate parabolic equations is extended to the pseudoprabolic case, and  degenerate pseudoparabolic equations with nonlinear integral operator are treated. Furthermore,  quasilinear equations, posed on time intervals of the form (-\infty,T], are considered. Some nonlinear pseudoparabolic equations are obtained as reduced form of systems of equations. To show existence, the Galerkin  and Rothe methods are used. The system of the degenerate equations is  solved using the   monotonicity and  gradient assumptions on the nonlinear function. The discretization along characteristics is applied to equations with convection. The existence of solutions of variational inequalities is proved by a penalty  method;  here  an inequality is replaced by an equation with an added penalty operator. The uniqueness follows from the monotonicity of the differential operators. In the case of  nonlinear pseudoparabolic equations, the uniqueness  can be shown for regular solutions only. The needed regularity is shown for two dimensional domains.
date: 2004
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/4802/1/Dissertation-PtashnykM.pdf
identifier: DOI:10.11588/heidok.00004802
identifier: urn:nbn:de:bsz:16-opus-48025
identifier:   Ptashnyk, Mariya  (2004) Nonlinear Pseudoparabolic Equations and Variational Inequalities.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/4802/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: ger