Thematic Session 3: Reaction-diffusion equations, new theoretical and applied trends

Cross-diffusion systems

Angela Stevens
University of Munster
Germany
Co-Author(s):    
Abstract:
Cross-diffusion systems play a major role in many applied contexts. One of the many interesting challenges is to classify parameter regimes for global existence or blow-up of their solutions. In order to prove global existence of solutions we introduce a new engergy functional, which is motivated by the transformation matrix given by Oelschlager in 1989, and which he used to rigorously derive cross-diffusion systems from moderately interacting stochastic many particle systems under the condition that the limiting PDE-system has regular solutions. We compare our findings with more recent results on the existence of solutions for cross-diffusion systems. (Joint work with Kyungeun Kang)