- 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.
Nonlinear Partial Differential Equations (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-81-13-M-7||Nonlinear Partial Differential Equations||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-TEMA] Industrial Mathematics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Nonlinear Partial Differential Equations
|P||84 h||186 h||-||-||PL1||9.0||irreg.|
- About [MAT-81-13-K-7]: Title: "Nonlinear Partial Differential Equations"; 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: 86325 ("Nonlinear PDE")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
In the exercise classes, the students have developed an experienced handling of the mathematical objects and methods that have been introduced and they have gained insights into interdisciplinary issues. They have learnt to apply these techniques to new problems, analyse them and to develop solution strategies.
- 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.
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)
- [MAT-80-11A-M-4] Numerics of ODE (M, 4.5 LP)