{"title":"Carleman Estimates and Exact Controllability Results for a Transmission System of two Nonconservative wave Equations","authors":"Carole Louis-Rose, Ali Perina, Louis Tebou","doi":"10.1007/s00245-025-10270-6","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a transmission system of two nonconservative wave equations with nonconstant coefficients in the one-dimensional setting. We investigate the exact (boundary and internal) controllability of this system using a single control. To solve these exact controllability problems, we rely on the duality approach which consists in proving inverse or observability inequality for the corresponding adjoint system. To prove these observability inequalities, we establish new Carleman estimates for the corresponding uncontrolled transmission system. These Carleman estimates require the introduction of new weight functions adapted to the coefficients of the principal operators. In particular, our Carleman estimates with internal observation are new in the framework of transmission systems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10270-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a transmission system of two nonconservative wave equations with nonconstant coefficients in the one-dimensional setting. We investigate the exact (boundary and internal) controllability of this system using a single control. To solve these exact controllability problems, we rely on the duality approach which consists in proving inverse or observability inequality for the corresponding adjoint system. To prove these observability inequalities, we establish new Carleman estimates for the corresponding uncontrolled transmission system. These Carleman estimates require the introduction of new weight functions adapted to the coefficients of the principal operators. In particular, our Carleman estimates with internal observation are new in the framework of transmission systems.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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