Journal of Inequalities and Applications 
Volume 6 (2001), Issue 1, Pages 37-55
doi:10.1155/S1025583401000042

Blowup of nonradial solutions to parabolic–elliptic systems modeling chemotaxis in two-dimensional domains

Toshitaka Nagai

 Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Received 15 October 1999; Revised 10 November 1999

Abstract

We consider the initial-boundary value problem of parabolic–elliptic systems on bounded domains in R2 with smooth boundary which is a mathematical model of chemotaxis. Making a differential inequality on the moment of solutions to the problem, we show the finite-time blowup of nonradial solutions under some condition on the mass and the moment of the initial data.