14.05.2025

Speaker: Peter Hirvonen Title:   How to Tackle Cross-Diffusion Systems

Abstract:   Cross-diffusion equations are used to model a wide range of naturally occurring phenomena, such as population dynamics or gas mixtures. However, the analysis of these is a difficult task, because of the complexity of interactions between species. In this talk, cross-diffusion systems are introduced and their mathematical difficulty is discussed. The concept and use of entropy functionals are outlined and shown with the help of two examples. In both cases, the focus of the presentation lies in showing the global existence of weak solutions, which therefore includes a showcase of standard tools in the field of nonlinear PDEs.