Energy methods in chemotaxis models
by
Vincent Calvez
Ecole Normale Superieure, Paris
Coauthors: Adrien Blanchet (WPI, Wien) Jose Carrillo (UAB, Barcelona)

The main question arising from chemotaxis models is whether cell density blows up or not in finite time. Particularly in dimension two, this behavior is subject to a mass threshold. Methods based on the corresponding free energy provide a good understanding of such systems.

In this talk we present two extensions of the classical Keller-Segel model, by changing respectively the equation driving the cell density and the one giving the chemical potential. For both models we show how the free energy method brings optimal results concerning the prevention of blow-up. Furthermore we describe a connection between the Keller-Segel model and recent advances in systems of interacting particles: a mass-transport steepest descent scheme is investigated.

Date received: June 19, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavg-22.