Differential Equations and Nonlinear Mechanics
Volume 2007 (2007), Article ID 87696, 16 pages
doi:10.1155/2007/87696
Research Article
Uniform Blow-Up Rates and Asymptotic Estimates of Solutions for Diffusion Systems with Nonlocal Sources
1Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, Jiangsu, China
2College of Zhongbei, Nanjing Normal University, Nanjing 210046, Jiangsu, China
Received 13 April 2006; Revised 27 November 2006; Accepted 19 December 2006
Academic Editor: Nicola Bellomo
Copyright © 2007 Zhoujin Cui and Zuodong Yang. 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
This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of |u(t)|∞ is precisely determined.