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

Zhoujin Cui1 and Zuodong Yang1,2

 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

Recommended by Nicola Bellomo

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.