LFU:online

The aim of this course is to give an introduction to the mathematical analysis of dispersive PDEs (including fractional Sobolev spaces and Strichartz estimates) and to gain a first understanding of the main problems that arise in the analysis of nonlinear models.

Nonlinear dispersive PDEs, such as the Schrödinger equation or  the wave equation, play a fundamental role in physics and applications. In general, nonlinear PDEs cannot not be solved explicitly (i.e. by a solution formula) and one has to rely on more sophisticated tools from functional analysis to analyse central questions such as the existence and uniqueness of solutions, regularity properties and long-time behaviour. In addition, nonlinear effects might lead to the formation of singularities, such that global in time existence cannot be guaranteed for all initial data.

An overview over all VU-type courses offered during the academic year (winter and summer term) can be found here: https://www.uibk.ac.at/mathematik/studium/masterstudium/