{"title":"Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term","authors":"Xinyu Mei, T. Sun, Yongqin Xie, Kaixuan Zhu","doi":"10.12775/tmna.2022.022","DOIUrl":null,"url":null,"abstract":"In this paper, based on a new theoretical framework of\ntime-dependent global attractors (Conti, Pata and Temam \\cite{CPT13}),\nwe consider the strongly damped wave equations $\\varepsilon(t)u_{tt}-\\Delta u_{t}-\\Delta u+f(u)=g(x)$\nand establish the existence of attractors\nin $\\mathcal{H}_{t}=H_{0}^{1}(\\Omega)\\times L^{2}(\\Omega)$\nand $\\mathcal{V}_{t}=H_{0}^{1}(\\Omega)\\times H_{0}^{1}(\\Omega)$, respectively.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2022.022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, based on a new theoretical framework of
time-dependent global attractors (Conti, Pata and Temam \cite{CPT13}),
we consider the strongly damped wave equations $\varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u)=g(x)$
and establish the existence of attractors
in $\mathcal{H}_{t}=H_{0}^{1}(\Omega)\times L^{2}(\Omega)$
and $\mathcal{V}_{t}=H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)$, respectively.
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