EXISTENCE AND UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC PLATE EQUATIONS WITH MULTIPLICATIVE NOISE ON $ \mathbb{R}^N $

Qiaozhen Ma; Xiaobin Yao; Tingting Liu

doi:10.11948/20200215

2021 Volume 11 Issue 3

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Qiaozhen Ma, Xiaobin Yao, Tingting Liu. EXISTENCE AND UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC PLATE EQUATIONS WITH MULTIPLICATIVE NOISE ON $ \mathbb{R}^N $[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1422-1454. doi: 10.11948/20200215

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Qiaozhen Ma, Xiaobin Yao, Tingting Liu. EXISTENCE AND UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC PLATE EQUATIONS WITH MULTIPLICATIVE NOISE ON $ \mathbb{R}^N $[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1422-1454. doi: 10.11948/20200215

EXISTENCE AND UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC PLATE EQUATIONS WITH MULTIPLICATIVE NOISE ON $ \mathbb{R}^N $

1.
College of Mathematics and Statistics, Northwest Normal University, AnningDong Road, Lanzhou 730070, China
2.
School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China

Corresponding author: Email address: lttnwnu91@126.com (T. Liu)
Fund Project: The authors were supported by National Natural Science Foundation of China (11961059, 11561064, 11761062)

Abstract

Abstract

Based on the abstract theory of random attractors of non-autonomous non-compact dynamical systems, we investigate existence and the upper semi-continuity of random attractors for the non-autonomous stochastic plate equations with multiplicative noise defined on the entire space $ \mathbb{R}^n $. We extend and improve the results of [42] not only from the additive white noise to the multiplicative white noise, but also from the time-independent of forcing term $ g(x) $ to the time-dependent forcing term $ g(x, t) $.
- Random attractor /
- stochastic plate equation /
- upper semi-continuity
MSC: 35B25, 35B40, 35B41, 37L30

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