{"title":"Null controllability for parabolic systems with dynamic boundary conditions","authors":"Mariem Jakhoukh, Lahcen Maniar","doi":"10.3934/eect.2023051","DOIUrl":null,"url":null,"abstract":"In this paper, we study the null controllability of systems of $ n $-coupled parabolic equations with dynamic boundary conditions, where the coupling and control matrices $ A $ and $ B $ are constant in time and space. Being different to the case of static boundary conditions, we will show that the Kalman rank condition $ rank[B, AB,\\dots, A^{n-1}B ] = n $ is a sufficient condition, we also show that it is necessary for the null controlability under an extra assumption on the boundary coupling. The null controlability result will be proved by proving Carleman and observability inequalities for the corresponding adjoint problem.","PeriodicalId":48833,"journal":{"name":"Evolution Equations and Control Theory","volume":"55 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations and Control Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/eect.2023051","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: 0
Abstract
In this paper, we study the null controllability of systems of $ n $-coupled parabolic equations with dynamic boundary conditions, where the coupling and control matrices $ A $ and $ B $ are constant in time and space. Being different to the case of static boundary conditions, we will show that the Kalman rank condition $ rank[B, AB,\dots, A^{n-1}B ] = n $ is a sufficient condition, we also show that it is necessary for the null controlability under an extra assumption on the boundary coupling. The null controlability result will be proved by proving Carleman and observability inequalities for the corresponding adjoint problem.
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