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Random attractors for Ginzburg-Landau equations driven by difference noise of a Wiener-like process. (English) Zbl 1459.35349

Summary: We consider a Wong-Zakai process, which is the difference of a Wiener-like process. We then prove that there are random attractors for non-autonomous Ginzburg-Landau equations driven by linear multiplicative noise in terms of Wong-Zakai process and Wiener-like process, respectively. Moreover, we establish the upper semi-continuity of random attractors as the size of difference noise tends to zero.

MSC:

35Q56 Ginzburg-Landau equations
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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