Nonlinear Pseudoparabolic Equations and Variational Inequalities

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2004

Author dc:creator

• Ptashnyk, Mariya

Contributors dc:contributor

• Jäger, Willi

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/4802

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:4802