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

Shouming Zhou; Chunlai Mu; Yongsheng Mi; Fuchen Zhang

doi:10.3934/cpaa.2013.12.2935

Article Contents

2013, Volume 12, Issue 6: 2935-2946. Doi: 10.3934/cpaa.2013.12.2935

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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

Received: November 2011

Revised: March 2012

Published: November 2013

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Abstract

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.

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Mathematics Subject Classification: 35B40, 45E10.

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