Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition
Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition
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DOI：
10.3934/cpaa.2013.12.2935
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发表时间：
2013-05
影响因子：
1
通讯作者：
Shouming Zhou;Chunlai Mu;Yongsheng Mi;Fuchen Zhang
中科院分区：
文献类型：
--
作者：
Shouming Zhou;Chunlai Mu;Yongsheng Mi;Fuchen Zhang
研究了一类带指数反应项的非局部扩散方程在Neumann边界条件下的爆破问题。得到了解的局部存在唯一性。此外，我们证明了方程的解在有限时间内爆破。在适当的假设下，我们给出了爆破率的估计，并得到了在原点有一个极大值的径向对称解的爆破集是一个单点x=0。最后，通过数值实验验证了我们的结论.
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.