The three lecture cycle will be devoted to boundary value problems for linear and
quasi-linear partial differential equations. The cycle will start with the review of classical
boundary value problems for equations of mathematical physics, in particular with the
Dirichlet problem for Laplace's equation and initial-boundary value problems for heat
and wave equations. The question of classication of linear partial differential equations
will be also discussed.
The main emphasis will be made on nonclassical initial-boundary and boundary value
problems and the methods of their investigation. The initial periodic and periodic boundary value problems for higher order linear and quasi-linear partial differential equations
will be considered as "model" problems. These model problems will be used to better
describe well-posed and ill-posed boundary value problems and differential properties of
Lecture 1 History of the matter: classical boundary value problems, well-posedness;
classication of partial differential equations; Holder spaces; Sobolev spaces.
Lecture 2 Nonclassical initial-boundary value problems for higher order hyperbolic
equations with two independent variables; well-posed problems; ill-posed problems.
Lecture 3 Nonclassical boundary value problems for higher order linear and quasi-linear
partial differential equations.
Předmět je dovoleno ukončit i mimo zkouškové období.
Předmět je vyučován jednorázově.
Výuka probíhá blokově.