Quenching for a reaction–diffusion equation with nonlinear memory ☆
Quenching for a reaction–diffusion equation with nonlinear memory ☆
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DOI：
10.1016/j.cnsns.2011.05.043
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发表时间：
2012-02
影响因子：
3.9
通讯作者：
Shouming Zhou;Chunlai Mu;Q. Du;Rong Zeng
中科院分区：
文献类型：
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作者：
Shouming Zhou;Chunlai Mu;Q. Du;Rong Zeng
研究了一类具有非线性记忆的反应扩散方程在Dirichlet正边界条件下的猝灭现象，其中p ≠ 0，q，α>0.证明了解的局部存在唯一性，并证明了存在临界长度α <$使得解在有限时间内猝灭，证明了时间导数在猝灭点处爆破.在适当的假设下，给出了猝灭速率的估计。最后，通过数值实验验证了我们的结果.
This paper is devoted to study the quenching phenomenon for a reaction–diffusion equation with nonlinear memory subject to positive Dirichlet boundary condition,where p⩾0, q, α>0. The local existence and uniqueness of the solution are proved, moreover, there exists a critical length α∗such that the solution quenches in finite time for α⩾α∗, and the blow-up of time-derivatives at the quenching point is verified. Under appropriate hypotheses, the quenching rate estimates are given. Finally, some numerical experiments are performed which illustrate our results.