LFU:online

Absolventinnen und Absolventen dieses Moduls verstehen die Inhalte der Vorlesung und können diese wiedergeben und anwenden.

Partial differential equations (PDEs) play a fundamental role in physics and applications. However, only in very simple cases PDEs can be solved explicitly (i.e. by a solution formula). In general one has to rely on more sophisticated tools (using functional analysis) in order to analyse central questions such as the existence and uniqueness of solutions, regularity properties and long-time behaviour. In addition, nonlinearities usually introduce highly non-trivial dynamics and the possible formation of singularities in finite time has to be taken into account.

In this lecture, we discuss some basic functional analytic tools and methods in the analysis of linear and nonlinear PDEs including a proper introduction of Sobolev spaces. 

Lecture, problems (homework) and discussions

Die Note setzt sich aus der Leistung im Übungsteil sowie einer schriftlichen Prüfung über den Vorlesungsstoff zusammen.

T. Tao: Nonlinear dispersive equations: Local and global analysis

M. Renardy, R. Rogers: An Introduction to Partial Differential Equations

aus dem Bachelor: Analysis 4, Partielle Differentialgleichungen