Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-81-13-K-7

Nonlinear Partial Differential Equations (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP
4 V Lecture 56 h 124 h
2 U Exercise class (in small groups) 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Livecycle-State [NORM] Active

Contents

  • Fundamentals: Weak convergence and compactness,
  • Elliptic Partial Differential Equations: weak solution theory (Lax-Milgram Theorem, Fredholmalternative), regularity (in the interior, to the edge), eigenvalue problems, maximum principles,
  • Evolution equations: Duality theory, weak convergence in Hilbert spaces, Gelfand triple,
  • Spaces of time-dependent functions, parabolic equations (weak formulation, existence and uniqueness, regularity, maximum principles), hyperbolic partial differential equations,
  • Calculus of variations,
  • Theory of monotone operators and fixed point theorems,
  • Approximations: iterations, space discretisation (Galerkin), time discretisation (Rothe), regularisations.

Literature

  • R.A. Adams: Sobolev Spaces,
  • H. Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations,
  • L.C. Evans: Partial Differential Equations,
  • G.M. Lieberman: Second Order Parabolic Partial Differential Equations,
  • M. Ruzicka: Nichtlineare Funktionalanalysis,
  • R. Showalter: Monotone operators in Banach space and nonlinear partial differential equations,
  • E. Zeidler: Nonlinear Functional Analysis and its Applications II/B: Nonlinear Mono-tone Operators.

Materials

Further literature will be announced in the lecture.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Course [MAT-81-13-K-7]

Module Name Context
[MAT-81-13-M-7] Nonlinear Partial Differential Equations P: Obligatory 4V+2U, 9.0 LP