Asymptotic properties of reaction-diffusion systems modeling chemotaxis

Abstract

This paper examines a system first introduced by Keller and Segel in 1970 to model the tendency of slime molds to move towards higher concentrations of a chemical which they themselves secrete. The paper particularly addresses the question of blow-up or chemotactic collapse, i.e., the formation of single point aggregations of the cells. Results are discussed for 2 and 3 space dimensions. Asymptotic computations yield information on the manner of the blow-up.