{"title":"低正则强迫项强阻尼波动方程的时变全局吸引子","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":"{\"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}","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}
Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term
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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