Convergence to traveling waves for time-periodic bistable reaction-diffusion equations

Ding, Weiwei

doi:10.1090/proc/15338

Convergence to traveling waves for time-periodic bistable reaction-diffusion equations
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Proc. Amer. Math. Soc. 149 (2021), 1647-1661 Request permission

Abstract:

We consider the equation $u_t=u_{xx} +f(t,u)$, $x\in \mathbb {R}$, $t>0$, 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.

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