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

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.