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Convergence to traveling waves for time-periodic bistable reaction-diffusion equations
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-02-09 , DOI: 10.1090/proc/15338 Weiwei Ding
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-02-09 , DOI: 10.1090/proc/15338 Weiwei Ding
Abstract:We consider the equation 
, 
, 
, where 
periodically depends on 
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.
中文翻译：
时间周期双稳态反应扩散方程的行波收敛
摘要：我们认为方程，，，其中周期性取决于是双稳态的类型。经典结果表明，对于一大类初始函数，如果解连接了两个线性稳定的时间周期状态，则解收敛到周期性行波。在初始函数的某些条件下，我们通过一种允许时间周期状态退化的新方法证明了这种收敛结果。
更新日期：2021-04-12
, , , where periodically depends on 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. 中文翻译：
时间周期双稳态反应扩散方程的行波收敛
摘要：我们认为方程，，，其中周期性取决于是双稳态的类型。经典结果表明，对于一大类初始函数，如果解连接了两个线性稳定的时间周期状态，则解收敛到周期性行波。在初始函数的某些条件下，我们通过一种允许时间周期状态退化的新方法证明了这种收敛结果。
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