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Random attractors for stochastic delay wave equations on $ \mathbb{R}^n $ with linear memory and nonlinear damping
Author(s) -
Jingyu Wang,
Yejuan Wang,
Lin Yang,
Tomás Caraballo
Publication year - 2021
Publication title -
discrete and continuous dynamical systems - s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021141
Subject(s) - attractor , uniqueness , mathematics , combinatorics , physics , mathematical analysis
A non-autonomous stochastic delay wave equation with linear memory and nonlinear damping driven by additive white noise is considered on the unbounded domain \begin{document}$ \mathbb{R}^n $\end{document} . We establish the existence and uniqueness of a random attractor \begin{document}$ \mathcal{A} $\end{document} that is compact in \begin{document}$ C{([-h, 0];H^1(\mathbb{R}^n))}\times C{([-h, 0];L^2(\mathbb{R}^n))}\times L_\mu^2(\mathbb{R}^+;H^1(\mathbb{R}^n)) $\end{document} with \begin{document}$ 1\leqslant n \leqslant 3 $\end{document} .

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