Module Handbook

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Module MAT-70-14-M-7

Nonlinear Functional Analysis with Applications to PDE (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-70-14-M-7 Nonlinear Functional Analysis with Applications to PDE 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

This module cannot be used together with the module [MAT-81-13-M-7] because of large content overlaps.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-70-14-K-7
Nonlinear Functional Analysis with Applications to PDE
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-70-14-K-7]: Title: "Nonlinear Functional Analysis with Applications to PDE"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86319 ("Nonlinear Functional Analysis with Applications to PDE")

Evaluation of grades

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


Contents

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.

Competencies / intended learning achievements

Upon successful completion of this module, the students master advanced methods and techniques, which play a central role especially in the analysis and solution of nonlinear elliptic and parabolic partial differential equations. They have also gained in-depth knowledge of the interaction and mutual influence of the theory and its applications. They are able to name the main propositions of the lecture, classify and explain the illustrated connections.

By studying concrete examples, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.

Literature

  • 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.

Requirements for attendance (informal)

Knowledge from the module [MAT-81-11-M-7] is desirable, but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-70-14-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.)