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Pullback attractors for the non-autonomous complex Ginzburg-Landau type equation with \(p\)-Laplacian. (English) Zbl 1418.35041
Summary: 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 \(L^2(\Omega)\cap W_0^{1,p}(\Omega)\cap L^q(\Omega)\) for the process \(\{U (t,\tau)\}_{t>\tau}\) corresponding to the non-autonomous complex Ginzburg-Landau type equation with \(p\)-Laplacian. Next, the existence of a pullback attractor in \(L^2(\Omega)\) is established by the Sobolev compactness embedding theorem. Finally, we prove the existence of a pullback attractor in \(W_0^{1,p}(\Omega)\) for the process \(\{U(t,\tau)\}_{t>\tau}\) by asymptotic a priori estimates.
MSC:
35B41 Attractors
35Q56 Ginzburg-Landau equations
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