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Volume 10, Number 6, 2020, Pages 2338-2361                                                                DOI:10.11948/20190215
Wong-Zakai approximations and attractors for fractional stochastic reaction-diffusion equations on unbounded domains
Yaqing Sun,Hongjun Gao
Keywords:Fractional reaction-diffusion equation, Wong-Zakai approximation, random attractor, upper semi-continuity, white noise.
Abstract:
      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.
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