Pullback attractor for a non-autonomous reaction-diffusion equation in some unbounded domains

Abstract

The existence of a pullback attractor in L2(Ω) for the following nonautonomous reaction-di usion equation ∂u ∂t − △u = f(u) + h(t), in Ω × (τ, +∞), u = 0, on ∂Ω × (τ, +∞), u(x, τ ) = uτ (x), x ∈ Ω, is proved in this paper, when the domain Ω is not necessarily bounded but satisfying the Poincaré inequality, and h ∈ L2 loc(R; H−1(Ω)). The main concept used in the proof is the asymptotic compactness of the process generated by the problem.