- 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).
Operator Semigroups and Applications to PDE (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-71-13-M-7||Operator Semigroups and Applications to PDE||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
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.
Competencies / intended learning achievements
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.
- 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.
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)