具有非局部源的反应扩散方程中解的消失行为

Extinction Behavior of Solutions for Reaction-Diffusion Equations with Nonlocal Sources

本文主要研究低维情形中具有非线性非局部源项和非线性内部吸收项的反应扩散方程的初边值问题,并利用积分模估计的方法得到其非负弱解的消失、非消失现象及其衰减估计。结果发现,在低维情形下非负弱解消失的临界指数不变,并且衰减估计值依赖于初始值、系数及区域的选取。

In this paper, we investigated the initial-boundary value problem of the reaction-diffusion equation with nonlocal nonlinear source and interior nonlinear absorption in the lower dimensional space and obtain the extinction, non-extinction and decay estimates of non-negative weak solutions by using integral norm estimate method. The result show that the critical extinction exponent keeps unchanged, and decay estimates depend on the choices of initial data, coefficients and domain.