{"title":"Dynamics of the quintic wave equation with nonlocal weak damping","authors":"Feng Zhou, Hongfang Li, Kaixuan Zhu, Xinyu Mei","doi":"arxiv-2409.10035","DOIUrl":null,"url":null,"abstract":"This article presents a new scheme for studying the dynamics of a quintic\nwave equation with nonlocal weak damping in a 3D smooth bounded domain. As an\napplication, the existence and structure of weak, strong, and exponential\nattractors for the solution semigroup of this equation are obtained. The\ninvestigation sheds light on the well-posedness and long-time behavior of\nnonlinear dissipative evolution equations with nonlinear damping and critical\nnonlinearity.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"143 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10035","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
This article presents a new scheme for studying the dynamics of a quintic
wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an
application, the existence and structure of weak, strong, and exponential
attractors for the solution semigroup of this equation are obtained. The
investigation sheds light on the well-posedness and long-time behavior of
nonlinear dissipative evolution equations with nonlinear damping and critical
nonlinearity.
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