GRK-Kolloquium, Prof. A. Jüngel

Titel:
Taming cross-diffusion systems with entropy methods

Abstract:
Many applications in physics and biology, like segregation of population
species, fluid mixtures, and tumor growth, can be described on the macroscopic
level by so-called cross-diffusion systems, which are systems of strongly
coupled parabolic equations. Often, the diffusion matrix of these models is
neither symmetric nor positive definite, but it becomes positive semidefinite
when formulated in terms of entropy variables. Then the entropy formulation
reveals a formal gradient-flow structure. This talk introduces to entropy
methods used to analyze cross-diffusion systems, including equations with
nonstandard degeneracies. Results comprise the global existence of solutions,
their boundedness and large-time behavior as well as weak-strong uniqueness. The
use of entropy methods is very extensive, also for the design of
structure-preserving numerical schemes and to treat stochastic noise terms.