Teachers

Norbert J. Mauser
Ulisse Stefanelli
Hans Peter Stimming

Schedule

Tuesdays 9.45-11.15, HS02 and Fridays 11:30-13:00, HS11,
Oskar-Morgenstern-Platz 1.

Aims

The course touches upon some aspects on some aspects of modern "Applied Analysis", namely "Asymptotic Analysis" and "Variational Methods".
Starting with the "scaling" of model equations we introduce regular and singular perturbation theory as a tool for asymptotic expansions in the context of "model hierarchies", like the transition from Burgers to Hopf equation or Boltzmann to Navier-Stokes to Euler equation.
We will also present an operative introduction to variational methods in analysis, with specific emphasis on existence theories, both in the linear and in the nonlinear setting. examples of application of discretization, monotonicity, and compactness methods will be presented.

Literature

• C. Schmeiser, "Angewandte Mathematik".
• C. Kuttler, "Mathematische Modellbildung".
• H. Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations", Springer, 2011.
• R. E. Showalter, "Maximal Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations", AMS, 1996.

The notes from the lectures are here: 1, 2, 3, 4, 5, 6.
A list of exercises can be found here