{"title":"The existence, asymptotic behaviour and blow-up of solution of a plate equation with nonlinear averaged damping","authors":"Hongwei Zhang, Ling Liu, Hongyun Yue, Donghao Li, Khaled Zennir","doi":"10.1016/S0034-4877(24)00081-8","DOIUrl":null,"url":null,"abstract":"<div><div>The initial boundary-value problem for a plate equation with nonlocal damping is considered. The local existence of solution is proved by the monotone operator theory with locally Lipschitz perturbation. By using the potential well theory, we get the global existence of solution. By Nakao's inequality, the decay estimate of polynomial type is obtained. We provide also the sufficient conditions of finite time blow-up of weak solutions with suitable conditions on the initial data by an ordinary differential inequality for an appropriately chosen functional.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 305-323"},"PeriodicalIF":1.0000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000818","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The initial boundary-value problem for a plate equation with nonlocal damping is considered. The local existence of solution is proved by the monotone operator theory with locally Lipschitz perturbation. By using the potential well theory, we get the global existence of solution. By Nakao's inequality, the decay estimate of polynomial type is obtained. We provide also the sufficient conditions of finite time blow-up of weak solutions with suitable conditions on the initial data by an ordinary differential inequality for an appropriately chosen functional.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
