Mathematik-Gebäude, Seminarraum M1011

We consider some versions of the Keller-Segel PDE system which are used in the modeling of the biological process of chemotaxis. Going beyond the classical, aka `minimal` Keller-Segel model, such more realistic models account for nonlinear diffusion mechanisms, for proliferation of cells, or for interaction with external components (such as the extracellular matrix), for instance. The goal of the talk is to survey on some recent analytical results on basic dynamical aspects such as global existence, boundedness, large time behavior, and blow-up of solutions. We also intend to point out some borderlines which currently cannot be crossed by mathematical analysis. These are linked to a number of open questions which, as we suspect, can be answered by means of an interplay between analysis and simulation.

Prof. Dr. Michael Winkler

Universität Dusiburg-Essen