Sep 12, 2019
Vortrag Forschungsseminar 18.09.2019
Prof. Dr. Jan-F. Pietschmann von der TU Chemnitz ist am 18.09.2019 zu Gast an unserem Institut und wird im Rahmen des Forschungsseminars einen Vortag zum Thema " Some remarks on a system of cross-diffusion equations with formal gradient flow structure" halten.
Abstract:
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.