Open AccessAsymptotic behavior of supercritical wave equations driven by colored noise on unbounded domains
Author(s) -
Bixiang Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021223
Subject(s) - sobolev space , uniqueness , attractor , bounded function , mathematics , operator (biology) , wave equation , supercritical fluid , colored , compact space , mathematical analysis , pure mathematics , physics , biochemistry , chemistry , materials science , repressor , transcription factor , composite material , gene , thermodynamics
This paper deals with the asymptotic behavior of the non-autonomous random dynamical systems generated by the wave equations with supercritical nonlinearity driven by colored noise defined on \begin{document}$ \mathbb{R}^n $\end{document} with \begin{document}$ n\le 6 $\end{document} . Based on the uniform Strichartz estimates, we prove the well-posedness of the equation in the natural energy space and define a continuous cocycle associated with the solution operator. We also establish the existence and uniqueness of tempered random attractors of the equation by showing the uniform smallness of the tails of the solutions outside a bounded domain in order to overcome the non-compactness of Sobolev embeddings on unbounded domains.