Random attractors of supercritical wave equations driven by infinite-dimensional additive noise on $  \mathbb{R}^n $

Jianing Chen; Bixiang Wang

doi:10.3934/dcdsb.2022093

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2023, Volume 28, Issue 1: 665-689. Doi: 10.3934/dcdsb.2022093

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Random attractors of supercritical wave equations driven by infinite-dimensional additive noise on $ \mathbb{R}^n $

Jianing Chen and
Bixiang Wang^,

Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

^* Corresponding author: Bixiang Wang
^* Corresponding author: Bixiang Wang

Received: January 31, 2022

Revised: February 28, 2022

Early access: May 2022

Published: January 2023

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In this paper, we prove the existence and uniqueness of tempered pullback random attractors of the supercritical stochastic wave equations driven by an infinite-dimensional additive white noise on $ \mathbb{R}^n $ with $ n\le 6 $. We first construct a tempered pullback random absorbing set in the natural energy space, and then establish the pullback asymptotic compactness of the solution operator by applying the idea of uniform tail-ends estimates as well as the uniform Strichartz estimates of solutions to circumvent the lack of compactness of Sobolev embeddings on unbounded domains.

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Mathematics Subject Classification: Primary: 35B40, 60H15; Secondary: 35R60, 35B41, 35L05.

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