Blow-Up of Solutions for a Class of Reaction-Diffusion Equations with a Gradient Term under Nonlinear Boundary Condition
Blow-Up of Solutions for a Class of Reaction-Diffusion Equations with a Gradient Term under Nonlinear Boundary Condition
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DOI：
10.5560/zna.2012-0048
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Junping Zhao
中科院分区：
文献类型：
--
作者：
Junping Zhao
研究了一类带梯度项的拟线性反应扩散方程ut = div（a（u）B（x）<$u）+ f（x;u;|拉乌|2; t）在非线性边界条件<$u=<$n+g（u）= 0下的解.通过构造一个新的辅助函数，利用Hopf极大值原理，得到了爆破解的存在性定理，爆破时间的上界和爆破速率的上估计.我们的结果表明，爆破时间T* 可能依赖于a（u），而与g（u）和f无关.
The blow-up of solutions for a class of quasilinear reaction-diffusion equations with a gradient term ut = div(a(u)b(x)▽u)+ f (x;u; |▽u|2; t) under nonlinear boundary condition ¶u=¶n+g(u) = 0 are studied. By constructing a new auxiliary function and using Hopf’s maximum principles, we obtain the existence theorems of blow-up solutions, upper bound of blow-up time, and upper estimates of blow-up rate. Our result indicates that the blow-up time T* may depend on a(u), while being independent of g(u) and f .