Pullback attractor for nonautonomous Ginzburg-Landau equation with additive noise. (English) Zbl 1474.37055

Summary: Long time behavior of stochastic Ginzburg-Landau equations with nonautonomous deterministic external forces, dispersion coefficients, and nonautonomous perturbations is studied. The domain is taken as a bounded interval \(\mathcal{I}\) in \(\mathbb{R}\). By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor in \(L^2(\mathcal{I})\) for the equation. The upper semicontinuity shows the stability of attractors under perturbations.


37H10 Generation, random and stochastic difference and differential equations
35B41 Attractors
35B40 Asymptotic behavior of solutions to PDEs
35R60 PDEs with randomness, stochastic partial differential equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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