Almost Automorphically and Almost Periodically Forced Circle Flows of Almost Periodic Parabolic Equations on S^1

Wenxian Shen, Yi Wang, Dun Zhou

We consider the skew-product semiflow which is generated by a scalar reaction-diffusion equation \begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in S^{1}=\mathbb{R}/2π\math…