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Journal of Mathematics
Volume 2013, Article ID 454513, 11 pages
http://dx.doi.org/10.1155/2013/454513
Research Article

Pattern Formation of a Keller-Segel Model with the Source Term

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

Received 31 January 2013; Accepted 11 August 2013

Academic Editor: Liwei Zhang

Copyright © 2013 Shengmao Fu and Fenli Cao. 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

Nonlinear dynamics near an unstable constant equilibrium in a Keller-Segel model with the source term is considered. It is proved that nonlinear dynamics of a general perturbation is determined by the finite number of linear growing modes over a time scale of , where is a strength of the initial perturbation.