Abstract for the talk on 29.01.2019 (15:15 h)
Oberseminar ANALYSIS - PROBABILITYJan-Frederik Pietschmann (TU Chemnitz)
Some remarks on a system of cross-diffusion equations with formal gradient flow structure
We study a system of cross-diffusion equations that results, as a
formal limit, from an interacting particle system with multiple
species. In the first part of the talk we exploit the (formal)
gradient flow structure of the system to prove the existence of weak
solutions. This is based on a priori bounds obtained from the
dissipation of the corresponding entropy and the use of dual
variables. In the second part, we discuss strong solutions and a
weak-strong stability result under certain conditions on the diffusion
constants.