Pullback random attractors of stochastic strongly damped wave equations with variable delays on unbounded domains

Li Yang; Li Yang

doi:10.3934/math.2021793

AIMS Mathematics

2021, Volume 6, Issue 12: 13634-13664. doi: 10.3934/math.2021793

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Research article

Pullback random attractors of stochastic strongly damped wave equations with variable delays on unbounded domains

Li Yang ^,

School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Received: 11 August 2021 Accepted: 23 September 2021 Published: 26 September 2021
MSC : 37L55, 35B41, 35B40

In this paper, we consider the asymptotic behavior of solutions to stochastic strongly damped wave equations with variable delays on unbounded domains, which is driven by both additive noise and deterministic non-autonomous forcing. We first establish a continuous cocycle for the equations. Then we prove asymptotic compactness of the cocycle by tail-estimates and a decomposition technique of solutions. Finally, we obtain the existence of a tempered pullback random attractor.
- strongly damped wave equation,
- variable delays,
- random attractor,
- asymptotical compactness,
- tail-estimates
Citation: Li Yang. Pullback random attractors of stochastic strongly damped wave equations with variable delays on unbounded domains[J]. AIMS Mathematics, 2021, 6(12): 13634-13664. doi: 10.3934/math.2021793

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Abstract

In this paper, we consider the asymptotic behavior of solutions to stochastic strongly damped wave equations with variable delays on unbounded domains, which is driven by both additive noise and deterministic non-autonomous forcing. We first establish a continuous cocycle for the equations. Then we prove asymptotic compactness of the cocycle by tail-estimates and a decomposition technique of solutions. Finally, we obtain the existence of a tempered pullback random attractor.

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