RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON $  {\mathbb{R}}^{N} $

Yanjiao Li; Xiaojun Li; Jiabin Zuo

doi:10.11948/20220006

2023 Volume 13 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(4): 1739-1765

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Yanjiao Li, Xiaojun Li, Jiabin Zuo. RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON $ {\mathbb{R}}^{N} $[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1739-1765. doi: 10.11948/20220006

Citation:

Yanjiao Li, Xiaojun Li, Jiabin Zuo. RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON $ {\mathbb{R}}^{N} $[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1739-1765. doi: 10.11948/20220006

RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON $ {\mathbb{R}}^{N} $

1.
Department of Mathematics, School of Science, Hohai University, Nanjing, 210098, China
2.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

Author Bio: Email: yanjiaoli2013@163.com(Y. Li); Email: zuojiabin88@163.com(J. Zou)
Corresponding author: Email: lixjun05@hhu.edu.cn (X. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 12271141, 11571092)

Abstract

Abstract

This paper investigates the long-time behavior of a stochastic strongly damped wave equation with additive noise on $ \mathbb{R}^{N} $. We establish that there exists a unique pullback random attractor for the equation in space $ H^1( {\mathbb{R}}^{N})\times L^2( {\mathbb{R}}^{N}) $ with the nonlinearity $ g(x,u) $ being of optimal subcritical growth $ p $: $ 1\leq p <p^*\equiv\frac{N+2}{(N-2)}(N\geq 3) $. In addition, we get the upper semicontinuity of the pullback random attractor as the intensity of noise goes to zero.
- Random attractors /
- upper semicontinuity /
- Stochastic wave equation /
- additive noise /
- unbounded domains
MSC: 37L55, 35B40, 37B55, 35B41

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