WONG-ZAKAI APPROXIMATIONS AND ATTRACTORS FOR FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS ON UNBOUNDED DOMAINS

Yaqing Sun; Hongjun Gao

doi:10.11948/20190215

2020 Volume 10 Issue 6

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Yaqing Sun, Hongjun Gao. WONG-ZAKAI APPROXIMATIONS AND ATTRACTORS FOR FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2338-2361. doi: 10.11948/20190215

Citation:

Yaqing Sun, Hongjun Gao. WONG-ZAKAI APPROXIMATIONS AND ATTRACTORS FOR FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2338-2361. doi: 10.11948/20190215

WONG-ZAKAI APPROXIMATIONS AND ATTRACTORS FOR FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS ON UNBOUNDED DOMAINS

Yaqing Sun¹,
Hongjun Gao^2, ,

1.
School of Mathematical Science, Jiangsu Provincial Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China
2.
Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China

Corresponding author: Email address: gaohj@hotmail.com (H. Gao)
Fund Project: The authors were supported by a NSFC Grant(No. 11531006), PAPD of Jiangsu Higher Education Institutions and Jiangsu Center for Collaborative Innovation in Geographica Information Resource Development and Application

Abstract

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.
- Fractional reaction-diffusion equation /
- Wong-Zakai approximation /
- random attractor /
- upper semi-continuity /
- white noise
MSC: 60H15, 37H10, 37L55, 37D10

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