Boundary Value Problems
Volume 2007 (2007), Article ID 64579, 12 pages
doi:10.1155/2007/64579
Research Article

Properties of Positive Solution for Nonlocal Reaction-Diffusion Equation with Nonlocal Boundary

Yulan Wang,1,2 Chunlai Mu,2 and Zhaoyin Xiang3

1School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China
2Department of Mathematics, Sichuan University, Chengdu 610064, China
3School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 21 January 2007; Accepted 11 April 2007

Academic Editor: Robert Finn

Copyright © 2007 Yulan Wang et al. 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 considers the properties of positive solutions for a nonlocal equation with nonlocal boundary condition u(x,t)=∫Ωf(x,y)u(y,t)dy on ∂Ω×(0,T). The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we establish the uniform blow-up estimates for the blow-up solution.