The boundary quenching behavior of a semilinear parabolic equation
The boundary quenching behavior of a semilinear parabolic equation
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DOI：
10.1016/j.amc.2011.05.002
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
Yuanhong Zhi
中科院分区：
文献类型：
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作者：
Yuanhong Zhi
在本文中，我们考虑一维空间中半线性抛物型问题的边界淬灭行为，其非线性同时出现在源项和诺伊曼边界条件中。首先，我们证明解在某个有限时间内在某个地方淬灭。然后我们断言，如果给定的初始数据是单调的，则猝灭只能发生在左边界上。最后我们得出了淬火时间附近溶液淬火速率的上限和下限。因此我们概括了我们以前的结果。
In this paper we consider the boundary quenching behavior of a semilinear parabolic problem in one-dimensional space, of which the nonlinearity appears both in the source term and in the Neumann boundary condition. First we proved that the solution quenches at somewhere in some finite time. Then we assert that the quenching can only occur on the left boundary if the given initial datum is monotone. Finally we derived the upper and lower bounds for the quenching rate of the solution near the quenching time. Thus we generalized our former results.