Pullback attractor for a non local non-autonomous evolution equation in an unbounded domain

Abstract

In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in ${\mathbb{R}}^N$ \[ \partial_t u=- u + g \left(β(J*u) +βh(t,u)\right) \] under some restrictions on $h$, growth restrictions on the nonlinear term $g$ and $\beta >1$. We prove, under suitable assumptions, existence, regularity and upper-semicontinuity of pullback attractors with respect to functional parameter $h(t)$ in some weighted spaces.