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- W2320798216 abstract "In this paper, we are concerned with the long-time behavior of the following non-autonomous quasi-linear complex Ginzburg-Landau equation with $p$-Laplacian begin{align*}frac{partial u}{partial t}-(lambda+ialpha)Delta_p u+(kappa+ibeta)|u|^{q-2}u-gamma u=g(x,t)end{align*}without any restriction on $q>2$ under additional assumptions. We first prove the existence of a pullback absorbing set in $L^2(Omega) cap W^{1,p}_0(Omega)cap L^q(Omega)$ for the process ${U(t,tau)}_{tgeq tau}$ corresponding to the non-autonomous quasi-linear complex Ginzburg-Landau equation (1)-(3) 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 $W^{1,p}_0(Omega)$ for the process ${U(t,tau)}_{tgeq tau}$ associated with the non-autonomous quasi-linear complex Ginzburg-Landau equation (1)-(3) with $p$-Laplacian by asymptotic a priori estimates." @default.
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- W2320798216 date "2014-01-01" @default.
- W2320798216 modified "2023-09-25" @default.
- W2320798216 title "Pullback attractors for the non-autonomous quasi-linear complex Ginzburg-Landau equation with $p$-Laplacian" @default.
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- W2320798216 doi "https://doi.org/10.3934/dcdsb.2014.19.1801" @default.
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