Uniform Attractors for Non-Autonomous Reaction-Diffusion Equation with Mixed Delay

Abstract

This paper is concerned with the asymptotic behavior of solutions of non-autonomous reaction-diffusion equation with delays. The well-posedness theory of equation for the initial data belonging to $C_{{L^r}(Ω)}$($1< r < ∞$) and $C_{{W^{1,r}}(Ω)}$($1< r < N$) is established respectively. In addition, the existence of uniform attractors in $C_{{L^r}(Ω)}$ for the family of processes with translation bounded external force is proved. Moreover, the long time behavior of solution with higher regularity in $C_{{W^{1,r}}(Ω)}$ is considered as well.