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}(\Omega)}(1<r<\infty)$ and $ C_{W^{1, r}(\Omega)}(1<r<N)$ is established respectively. In addition, the existence of uniform attractors in $ C_{L^{r}(\Omega)}$ 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}(\Omega)}$ is considered as well.

Keywords

Uniform attractors / reaction-diffusion equation with delays / non-autonomous equation