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

Recommended by Robert Finn

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.