Timeslots:

Monday, April 1st, 3 pm until 4.30 pm, SR15, 3rd floor, Oskar-Morgenstern-Platz 1

Tuesday, April 2nd, 10.30 am until 12.00 pm, SR11, 2nd floor, OMP1

Wednesday, April 3rd, 10.30 am until 12.00 pm, SR5, 1st floor, OMP1

Thursday, April 4th, 10.30 am until 12.00 pm, SR5, 1st floor, OMP1

Friday, April 5th, 9 am until 10.30 am, SR14, 2nd floor, OMP1

Abstract:

Cross-diffusion systems where introduced 40 years ago as a tool of modeling in the context of population dynamics. At the mathematical level, these systems happen to be surprisingly hard to study ; global (weak) solutions for the most simple of those were (only) built in 2006 even though they have been studied since the eighties.

We will start this lecture with a short introduction to present the model of Shigesada-Kawasaki-Teramoto (SKT, the first instance of cross-diffusion in the literature) and present (without proof) the existing results and the open questions related to it. Then, in the first part of the lecture, we will focus on the Kolmogorov equation, studying existence and uniqueness with the help of the duality lemma. In the second part of the lecture we will establish a global existence result for SKT systems, using a generalization of the entropy introduced by Chen and Jüngel in 2006, the duality lemma and a specific approximation procedure.