Hassan Messaoudi, Salah Zitouni, Houssem Eddine Khochemane, Abdelouaheb Ardjouni
{"title":"General stability for piezoelectric beams with a nonlinear damping term","authors":"Hassan Messaoudi, Salah Zitouni, Houssem Eddine Khochemane, Abdelouaheb Ardjouni","doi":"10.1007/s11565-022-00443-4","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, we consider the one-dimensional system of piezoelectric beams with a nonlinear damping term. First, we show the existence and uniqueness of solutions by the semi-group technique more precisely by Hille-Yosida theorem. And by building an appropriate Lyapunov functional, we establish general decay results for the solution of the system whose exponential and polynomial decays are only special cases. Moreover, our results does not depend on any relation between the parameters of the system.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"69 2","pages":"443 - 462"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-022-00443-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
In this article, we consider the one-dimensional system of piezoelectric beams with a nonlinear damping term. First, we show the existence and uniqueness of solutions by the semi-group technique more precisely by Hille-Yosida theorem. And by building an appropriate Lyapunov functional, we establish general decay results for the solution of the system whose exponential and polynomial decays are only special cases. Moreover, our results does not depend on any relation between the parameters of the system.
期刊介绍：
Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.
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