Pullback attractors for a non-autonomous semilinear degenerate parabolic equation

Abstract

In this paper, we consider the pullback attractors for a non-autonomous semilinear degenerate parabolic equation $u_{t}-{\rm div}(\sigma(x)\nabla u)+ f(u)=g(x,t)$ defined on a bounded domain $\Omega\subset \mathbb{R}^N$ with smooth boundary. We provide that the usual $(L^{2}(\Omega), L^{2}(\Omega))$ pullback $\mathscr{D}_{\lambda}$-attractor indeed can attract the $\mathscr{D}_{\lambda}$-class in $L^{2+\delta}(\Omega)$, where $\delta \in [0, \infty)$ can be arbitrary.