A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

摘要

In this paper we consider the strongly damped wave equation with time-dependent terms utt-Δu-γ(t)Δu t+βε(t)ut=f(u), in a bounded domain Ω??n, under some restrictions on β ε(t), γ(t) and growth restrictions on the nonlinear term f. The function βε(t) depends on a parameter ε, βε(t) →ε→00. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {Aε(t):t ∈ ?