Upper semicontinuity of pullback attractors for a non-autonomous viscoelastic equation

This paper is concerned with upper semicontinuity of pullback attractors, for a non-autonomous viscoelastic equation with a past history with a nonautonomous perturbation. In particular, under some proper assumptions, we prove that, the pullback attractor {Aε(t)}t∈R{Aε(t)}t∈R of Eq. (1.1) with ε>0ε>0 and the global attractor A of Eq. (1.1) with ε=0ε=0 satisfy limε→0+distX(Aε(t),A)=0limε→0+distX(Aε(t),A)=0 for any t∈Rt∈R.