Nonlinear Functional Analysis with Applications to PDE (2V, 4.5 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|2||V||Lecture||4.5 CP||28 h||107 h|
|(2V)||4.5 CP||28 h||107 h|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
This course cannot be used together with the course [MAT-81-13-K-7] because of large content overlaps.
From the large field of nonlinear functional analysis, methods and techniques are discussed which play a central role in the investigation of nonlinear elliptic and parabolic partial differential equations. In particular, the following contents are discussed:
- fixed point theorems,
- integration and differentiation in Banach spaces,
- the theory of monotone operators and their applications in the study of nonlinear elliptic and parabolic partial differential equations.
- H. W. Alt: Lineare Funktionalanalysis,
- H. Gajewski, K. Gröger, K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen,
- D. Gilbert, N. S. Trudinger: Elliptic partial differential equations of second order,
- E. Hille, S. Phillips: Functional analysis and semigroups,
- M. Ruzicka: Nichtlineare Funktionalanalysis: Eine Einführung,
- R. E. Showalter: Monotone operators in Banach space and nonlinear partial differential equations,
- K. Yoshida: Functional analysis,
- E. Zeidler: Nonlinear functional analysis and its applications I: Fixed-point theorems,
- E. Zeidler: Nonlinear functional analysis and its applications II/B.
Further literature will be announced in the lecture.
Requirements for attendance (informal)
Knowledge from the module [MAT-81-11-M-7] is desirable, but not necessarily required.
- [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)
- [MAT-80-11B-M-4] Introduction to PDE (M, 4.5 LP)
Requirements for attendance (formal)None
References to Course [MAT-70-14-K-7]
|[MAT-70-14-M-7]||Nonlinear Functional Analysis with Applications to PDE||P: Obligatory||2V, 4.5 LP|