Modeling and analysis of multi-species systems in biology

Multispecies systems arising in cell biology, population dynamics etc. may be
described by reaction-diffusion equations involving cross-diffusion terms.
Cross diffusion often reveals surprising effects such as uphill diffusion and
diffusion-induced instabilities, seemingly contradicting our intuition on diffusion.
Major difficulties of the mathematical analysis of the cross-diffusion systems
are their highly nonlinear structure and the lack of positive definiteness of the
diffusion matrix. In this talk, the boundedness-by-entropy method will be detailed,
which is inspired by thermodynamics and which allows for global existence and
boundedness results for large classes of cross-diffusion systems.