Prof. Dr. A. Jüngel (Technische Universität Wien, Österreich)
Wednesday, October 23, 2019 - 14:00
Weierstraß-Institut
Mohrenstr. 39, 10117 Berlin, Erhard-Schmidt-Hörsaal, Erdgeschoss
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Many real-world applications consist of multiple components, leading on the macroscopic scale to cross-diffusion systems which consist of strongly coupled parabolic equations. The applications may be very diverse and range from spin-polarized transport in semiconductors and ion transport in cell membranes to population dynamics. In this talk, some existence results for global-in-time weak solutions is proved, based on entropy methods. This technique was already used by Herbert Gajewski, and we detail some of his ideas to prove the large-time behavior and uniqueness of weak solutions, followed by some extensions like boundedness-by-entropy and martingale solutions to stochastic cross-diffusion systems.
submitted by eismann (andrea.eismann@wias-berlin.de, 030 20372320)