Journal of Applied Mathematics
Volume 2012 (2012), Article ID 648067, 17 pages
http://dx.doi.org/10.1155/2012/648067
Research Article

Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption

Yulan Wang,1 Zhaoyin Xiang,2 and Jinsong Hu1

1School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 21 January 2012; Accepted 20 April 2012

Academic Editor: Junjie Wei

Copyright © 2012 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

We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.