Dynamics of time-periodic reaction-diffusion equations with front-like initial data on $\mathbb{R}$

Weiwei Ding, Hiroshi Matano

This paper is concerned with the Cauchy problem $$u_t=u_{xx}+f(t,u),x\in \mathbb{R},t>0,$$ $$u(0,x)=u_0(x),x\in \mathbb{R},$$ where $f$ is a rather general nonli…