Asymptotic behavior for a class of non autonomous non local problems

Abstract

In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partial_t u =- u + g \left(β(t)(Ku) \right)\ \ \mbox{in}\ \ Ω,\\ u = 0\ \ \mbox{in}\ \ \mathbb{R}^N\backslashΩ, \end{cases} \] where $\Omega$ is a smooth bounded domain in ${\mathbb{R}}^N$, $\beta$ denotes the functional parameter given by a continuous bounded function on $\mathbb{R}$, and $K$ is an integral operator with symmetric kernel. We prove existence and some regularity properties of the pullback attractor.