Pullback attractors for the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian

Abstract

In this paper, we are concerned with the long-time behavior of the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. We first prove the existence of pullback absorbing sets in L²(Ω)∩W₀^1,p(Ω)∩L^q(Ω) for the process {U(t,τ)}_t⩾τ corresponding to the non-autonomous complex Ginzburg–Landau type equation with p-Laplacian. Next, the existence of a pullback attractor in L²(Ω) is established by the Sobolev compactness embedding theorem. Finally, we prove the existence of a pullback attractor in W₀^1,p(Ω) for the process {U(t,τ)}_t⩾τ by asymptotic a priori estimates.