Abstract and Applied Analysis
Volume 2006 (2006), Article ID 81265, 23 pages
Existence of global solution and nontrivial steady states for a system modeling chemotaxis
1School of Information and Electronics Engineering, Shandong Institute of Business and Technology, Yantai 264005, Shandong, China
2Department of Mathematics, Jackson State University, Jackson 39217, MS, USA
Received 23 March 2006; Revised 18 September 2006; Accepted 19 September 2006
Copyright © 2006 Zhenbu Zhang. 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.
We consider a reaction-diffusion system modeling chemotaxis,
which describes the situation of two species of bacteria competing for the same
nutrient. We use Moser-Alikakos iteration to prove the global existence of the solution. We
also study the existence of nontrivial steady state solutions and their stability.