{"title":"General stability of abstract thermoelastic system with infinite memory and delay","authors":"Jianghao Hao, Junna Zhang","doi":"10.3934/mcrf.2020040","DOIUrl":null,"url":null,"abstract":"In this paper we study an abstract thermoelastic system in Hilbert space with infinite memory and time delay. Under some suitable conditions, we prove the well-posedness by invoking semigroup theory. Since the damping may stabilize the system while the delay may destabilize it, we discuss the interaction between the damping and the delay term, and obtain that the system is uniformly stable when the effect of damping is greater than that of time delay. By establishing suitable Lyapunov functionals which are equivalent to the energy of system we also establish the general energy decay results for abstract thermoelastic system.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"82 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Control and Related Fields","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/mcrf.2020040","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper we study an abstract thermoelastic system in Hilbert space with infinite memory and time delay. Under some suitable conditions, we prove the well-posedness by invoking semigroup theory. Since the damping may stabilize the system while the delay may destabilize it, we discuss the interaction between the damping and the delay term, and obtain that the system is uniformly stable when the effect of damping is greater than that of time delay. By establishing suitable Lyapunov functionals which are equivalent to the energy of system we also establish the general energy decay results for abstract thermoelastic system.
期刊介绍：
MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.
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