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Wong-Zakai approximations and attractors for fractional stochastic reaction-diffusion equations on unbounded domains. (English) Zbl 1483.37096

Summary: In this paper, we investigate the Wong-Zakai approximations induced by a stationary process and the long term behavior of the fractional stochastic reaction-diffusion equation driven by a white noise. Precisely, one of the main ingredients in this paper is to establish the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of fractional stochastic reaction-diffusion equations. Thereafter the upper semi-continuity of attractors for the Wong-Zakai approximation of the equation as \(\delta\rightarrow0\) is proved.

MSC:

37L55 Infinite-dimensional random dynamical systems; stochastic equations
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35R11 Fractional partial differential equations
35K57 Reaction-diffusion equations
26A33 Fractional derivatives and integrals
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