Blow up of solutions of semilinear heat equations in general domains
Blow up of solutions of semilinear heat equations in general domains
复制标题
一般域中半线性热方程解的爆炸
DOI：
10.1142/s0219199713500429
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发表时间：
2013
影响因子：
1.6
通讯作者：
B. Sciunzi
中科院分区：
文献类型：
--
作者：
V. Marino;F. Pacella;B. Sciunzi
考虑非线性热方程Vt - Δv =| v| p-1v在有界光滑区域Ω n（n > 2）中的Dirichlet边界条件.在适当的假设条件下，给出了一个变号平稳古典解，证明了当满足以下条件时，|-1|> 0是足够小的，并且如果p足够接近临界指数。由于对于n = 1，解是全局的，这表明，一般来说，解是全局的初始数据集相对于原点不是星形的。这种现象以前已经观察到的情况下，当域是一个球和固定的解决方案是径向对称的。
Consider the nonlinear heat equation vt - Δv = |v|p-1v in a bounded smooth domain Ω ⊂ ℝn with n > 2 and Dirichlet boundary condition. Given up a sign-changing stationary classical solution fulfilling suitable assumptions, we prove that the solution with initial value ϑup blows up in finite time if |ϑ - 1| > 0 is sufficiently small and if p is sufficiently close to the critical exponent . Since for ϑ = 1 the solution is global, this shows that, in general, the set of the initial data for which the solution is global is not star-shaped with respect to the origin. This phenomenon had been previously observed in the case when the domain is a ball and the stationary solution is radially symmetric.