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)∩W01,p(Ω)∩Lq(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 W01,p(Ω) for the process {U(t,τ)}t⩾τ by asymptotic a priori estimates.

Keywords

• pullback attractor
• non-autonomous
• p-laplacian
• complex Ginzburg–Landau type equations
• Sobolev compactness embedding theorem
• asymptotic a priori estimates