Mathematical Analysis of Linear PDEs (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||9.0 CP||186 h|
|2||U||Exercise class (in small groups)||28 h|
|(4V+2U)||9.0 CP||84 h||186 h|
- revision of topics from functional analysis (linear spaces, dual spaces and weak convergence, compact operators, embedding, Fredholm theory, boundaries and regularity); crash course on Sobolev spaces (weak derivatives, definition of Sobolev spaces, approximation by smooth functions, traces, Sobolev inequalities and embedding, Poincaré inequalities),
- elliptical linear PDE of second order: existence of solutions via the Lax-Milgram theorem, the Fredholm alternative, spectral theory, inner regularity, regularity up to the boundary, maximum principles (weak and strong),
- parabolic linear PDE of second order: Sobolev spaces involving time, Bochner spaces, existence of weak solutions for parabolic PDE of second order via Galerkin approximations and via the Rothe method, uniqueness, regularity, maximum principles (weak and strong),
- hyperbolic linear PDE of second order: existence of weak solutions via energy estimates and compactness, uniqueness, regularity.
- H. W. Alt: Lineare Funktionalanalysis,
- L.C. Evans: Partial Differential Equations,
- H. Brezis: Functional Analysis, Sobolev Spaces, and Partial Differential Equations.
Further literature will be announced in the lecture; Exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-70-11-M-4] Functional Analysis (M, 9.0 LP)
Requirements for attendance (formal)
References to Course [MAT-81-36-K-7]
|[MAT-81-36-M-7]||Mathematical Analysis of Linear PDEs||P: Obligatory||4V+2U, 9.0 LP|