Module Handbook

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Module MAT-71-13-M-7

Operator Semigroups and Applications to PDE (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-71-13-M-7 Operator Semigroups and Applications to PDE 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-SPAS] Analysis and Stochastics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-71-13-K-7
Operator Semigroups and Applications to PDE
P 84 h 186 h - - PL1 9.0 irreg.
  • About [MAT-71-13-K-7]: Title: "Operator Semigroups and Applications to PDE"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86349 ("Operator Semigroups and Applications to PDE")

Evaluation of grades

The grade of the module examination is also the module grade.


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).

Competencies / intended learning achievements

Upon successful completion of this module, the students have gained advanced knowledge in one specific area of functional analysis, including applications in current fields of research (amongst others in the field of differential equations and mathematical physics).They are able to name the essential propositions of the lecture, classify and explain the illustrated connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

By solving the given exercise problems, they have gained a precise and independent handling of terms, propositions and methods of the lecture. In addition, they have learn to apply the methods to new problems, analyze them and develop solution strategies independently or by team work.

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.

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 Module / Module Number [MAT-71-13-M-7]

Module-Pool Name
[MAT-70-MPOOL-7] Specialisation Stochastic Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)