非线性反应扩散方程解的Blow-up问题

来源期刊：中南大学学报(自然科学版)2004年第4期

论文作者：刘金枝

文章页码：694 - 696

关键词：非线性反应扩散方程;初边值问题;光滑解; Blow-up问题

Key words：nonlinear reaction-diffusion equation; initial-boundary value problem; smooth solution;Blow-up behavior

摘    要：研究了非线性反应扩散方程u_t =Δu+f(u)初边值问题的解的Blow-up问题,证明了其光滑解只能在一个有界区间内存在。利用引入的“高斯函数”得到了一些新的非整体存在的充分条件,这些条件对L^p解也普遍适用。此外,对有关结果进行了相应的简化与改进。

Abstract: This paper studies the Blow-up behavior of the initial-boundary value problem for the nonlinear reaction-diffusion equation: u_t=Δu+f(u), and proves that the smooth solutions can only exist in a limited extent of time. Some new sufficient conditions for the nonexistence of the global solutions are obtained using Gauss function. These conditions are also suitable to L^p solution.