4 papers
Non-wandering points for autonomous/periodic parabolic equations on the circle
Wenxian Shen, Yi Wang, Dun Zhou
We study the properties of non-wandering points of the following scalar reaction-diffusion equation on the circle , \begin{equation*} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in…
Almost automorphically forced flows on or in one-dimensional almost periodic semilinear heat equations
Wenxian Shen, Yi Wang, Dun Zhou
In this paper, we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost-periodically forced scalar reaction-diffusion equation \begin…
Spatial-Homogeneity of Stable Solutions of Almost-Periodic Parabolic Equations with Concave Nonlinearity
Yi Wang, Jianwei Xiao, Dun Zhou
We study the spatial-homogeneity of stable solutions of almost-periodic parabolic equations. It is shown that if the nonlinearity satisfies a concave or convex condition, then any…
Asymptotic behavior of semilinear parabolic equations on the circle with time almost-periodic/recurrent dependence
Wenxian Shen, Yi Wang, Dun Zhou
We study topological structure of the -limit sets of the skew-product semiflow generated by the following scalar reaction-diffusion equation \begin{equation*} u_{t}=u_{xx}+f(t,u…