# American Institute of Mathematical Sciences

November  2013, 12(6): 2935-2946. doi: 10.3934/cpaa.2013.12.2935

## Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition

 1 College of Mathematics and statistics, Chongqing University, Chongqing 401331, China, China, China, China

Received  November 2011 Revised  March 2012 Published  May 2013

This paper deals with the blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition. The local existence and uniqueness of the solution are obtained. Furthermore, we prove that the solution of the equation blows up in finite time. Under appropriate hypotheses, we give the estimates of the blow-up rate, and obtain that the blow-up set is a single point $x=0$ for radially symmetric solution with a single maximum at the origin. Finally, some numerical experiments are performed, which illustrate our results.
Citation: Shouming Zhou, Chunlai Mu, Yongsheng Mi, Fuchen Zhang. Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2935-2946. doi: 10.3934/cpaa.2013.12.2935
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