Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition
Shouming Zhou, Chunlai Mu, Yongsheng Mi, Fuchen Zhang · Communications on Pure & Applied Analysis · 2013
This paper deals with the blow-up for a non-local diffusion equationwith exponential reaction term and Neumann boundary condition. Thelocal existence and uniqueness of the solution are obtained.Furthermore, we prove that the solution of the equation blows up infinite time. Under appropriate hypotheses, we give the estimatesof the blow-up rate, and obtain that the blow-up set is a singlepoint $x=0$ for radially symmetric solutionwith a single maximum at the origin. Finally, some numerical experiments are performed, which illustrate our results.