Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-71-13-K-7

Operator Semigroups and Applications to PDE (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 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 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-SPAS] Analysis and Stochastics
Additional informations
Livecycle-State [NORM] Active

Contents

  • definitions, generators, resolvents, examples,
  • Hille-Yosida theorem, Lumer-Phillips theorem,
  • contraction semigroups, analytic semigroups, operator groups,
  • approximations, perturbations,
  • applications to partial differential equation (including heat equation, wave equation, Schrödinger equation).

Literature

  • E.B. Davies: One Parameter Semigroups,
  • K.-J. Engel, R. Nagel: A Short Course on Operator Semigroups,
  • K.-J. Engel, R. Nagel: One-Parameter Semigroups for Linear Evolution Equations,
  • J. Goldstein: Semigroups of Linear Operators and Applications,
  • A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

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

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-71-13-K-7]

Module Name Context
[MAT-71-13-M-7] Operator Semigroups and Applications to PDE P: Obligatory 4V+2U, 9.0 LP