{"title":"线性动态反馈控制下波动方程传递问题的指数镇定","authors":"Zhiling Guo, Shugen Chai","doi":"10.3934/eect.2022001","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.</p>","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"18 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control\",\"authors\":\"Zhiling Guo, Shugen Chai\",\"doi\":\"10.3934/eect.2022001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.</p>\",\"PeriodicalId\":48833,\"journal\":{\"name\":\"Evolution Equations and Control Theory\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Evolution Equations and Control Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/eect.2022001\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/eect.2022001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control
In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.
期刊介绍:
EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include:
* Modeling of physical systems as infinite-dimensional processes
* Direct problems such as existence, regularity and well-posedness
* Stability, long-time behavior and associated dynamical attractors
* Indirect problems such as exact controllability, reachability theory and inverse problems
* Optimization - including shape optimization - optimal control, game theory and calculus of variations
* Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s)
* Applications of the theory to physics, chemistry, engineering, economics, medicine and biology