CONVERGENCE TO TRAVELING WAVES FOR TIME-PERIODIC BISTABLE REACTION-DIFFUSION EQUATIONS

被引：5

作者：

Ding, Weiwei ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Traveling waves; time-periodicity; reaction-diffusion equations; bistable nonlinearity; FRONTS; MONOTONICITY; DYNAMICS;

D O I：

10.1090/proc/15338

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the equation u(t) = u(xx) + f(t,u), x is an element of R, t > 0, where f(t, x) periodically depends on t and is of bistable type. Classical results showed that for a large class of initial functions, the solutions converge to a periodic traveling wave if it connects two linearly stable time-periodic states. Under some conditions on the initial functions, we prove this convergence result by a new approach which allows the time-periodic states to be degenerate.

引用

页码：1647 / 1661

页数：15

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