Kinetic Models for Chemotaxis and their Drift-Diffusion Limit

Chemotaxis is a process in which bacteria, or, more generally, cells, change their state of movement, reacting to the presence of a chemical substance, approaching chemically favorable environments and avoiding unfavorable ones.

In this talk, we rigorously prove that a kinetic model for chemotaxis introduced by Othmer, Dunbar and Alt has as its drift-diffusion limit the celebrated Keller-Segel model. Furthermore, we show that finite-time-blow-up, which generally occurs in the Keller-Segel model, does not occur in the kinetic model under certain biologically relevant assumptions on the turning kernel.