PřF:MNBVP Noncl. bound. v. prob. for PDE

MNBVP Nonclassical boundary value problems for partial differential equations

Přírodovědecká fakulta
podzim 2011

Rozsah

6/0. 1 kr. Ukončení: k.

Vyučující

Dr. Tariel Kiguradze (přednášející), doc. RNDr. Bedřich Půža, CSc. (zástupce)

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Osnova

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 their solutions.
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.

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