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The asymptotic behavior of the stochastic Ginzburg-Landau equation with additive noise. (English) Zbl 1139.65007

Summary: We show that the stochastic Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random dynamic system. Then we prove that the system possesses a compact random attractor in \(L^{2}(D)\) when the spatial dimension of \(D\) is one and two, respectively.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
35F05 Linear first-order PDEs
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