Prof. Dr. Martin Burger, DESY und Universität Hamburg

In this talk we will discuss some models for multicomponent drift-diffusion, which are mathematically challenging due to nonlinear cross-diffusion effects. Those lead to degeneracies on the one hand, preventing the use of standard methods for parabolic systems, and moreover do not possess any maximum or comparison principles. In order to derive a suitable mathematical theory and consistent models, gradient flow techniques are a key tool, which we will highlight in this talk. In particular we shall discuss the use of entropy dissipation methods and boundedness-by-entropy principles, finally we shall also give a view on pattern formation abilities.