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Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains II: The monotone case

Journal of Mathematical Physics, ISSN: 0022-2488, Vol: 59, Issue: 2
2018
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In this article, we continue the study of the dynamics of the following complex Ginzburg-Landau equation u - (λ + iα)Δu + (κ + iβ)|u|u - γu = f(t) on non-cylindrical domains. We assume that the spatial domains are bounded and increase with time, which is different from the diffeomorphism case presented in Zhou and Sun [Discrete Contin. Dyn. Syst., Ser. B 21, 3767-3792 (2016)]. We develop a new penalty function to establish the existence and uniqueness of a variational solution satisfying energy equality as well as some energy inequalities and prove the existence of a D-pullback attractor for the non-autonomous dynamical system generated by this class of solutions.

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