Bochra Belhadji , Mama Abdelli , Akram Ben Aissa , Khaled Zennir
{"title":"Global existence and stabilization of the quasilinear Petrovsky equation with localized nonlinear damping","authors":"Bochra Belhadji , Mama Abdelli , Akram Ben Aissa , Khaled Zennir","doi":"10.1016/j.jmaa.2024.129087","DOIUrl":null,"url":null,"abstract":"<div><div>We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129087"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24010096","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a locally nonlinear damped plate equation in a bounded domain where the damping is effective only in a neighborhood of a suitable subset of the boundary. Using the Faedo-Galerkin method, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the localization of the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
期刊介绍：
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
• Combinatorics
• Mathematical physics.
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
