Partielle Differentialgleichungen II
Montag 14-16, Dienstag, 14-16
Raum 04-522
The lectures will be given in English. The contents correspond to those which are given in the module handbook for this course. The aim is to learn essential techniques which are important for working with partial differential equations. Distributions in the sense of Laurent Schwartz are introduced. These objects are generalizations of functions which are in a certain sense less regular. The most famous example is the Dirac delta function, which is not a function in the literal sense. Distributions are most useful for linear partial differential equations. Various function spaces are introduced, in particular Hölder and Sobolev spaces, which are a natural habitat for the solutions of partial differential equations. It is explained what side conditions (initial and boundary conditions) can reasonably be required for different partial differential equations. Notions of weak solutions are described where the equations are not satisfied pointwise. This theme is closely related to the theory of distributions. It is explained how these general techniques are applied to concrete equations and how in turn these concrete equations can be applied to model phenomena in the natural sciences.