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The asymptotic behavior of the stochastic Ginzburg-Landau equation with multiplicative noise. (English) Zbl 1064.37038

Summary: The asymptotic behavior of the stochastic Ginzburg–Landau equation is studied. We obtain the stochastic Ginzburg–Landau equation as a finite-dimensional random attractor.

MSC:

37H10 Generation, random and stochastic difference and differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35R60 PDEs with randomness, stochastic partial differential equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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References:

[1] DOI: 10.3934/dcds.2000.6.875 · Zbl 1011.37031 · doi:10.3934/dcds.2000.6.875
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