Differential Equations and Nonlinear Mechanics
Volume 2007 (2007), Article ID 87696, 16 pages
doi:10.1155/2007/87696
Uniform blow-up rates and asymptotic estimates of solutions for diffusion systems with nonlocal sources
Zhoujin Cui
and Zuodong Yang
Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, Jiangsu, China
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.