Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability

Tatsien Li; Bopeng Rao

doi:10.5802/crmath.341

Théorie du contrôle

Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability
[Théorème d’unicité pour un système d’équations des ondes avec observation interne incomplète et application à la contrôlabilité approachée]

Tatsien Li ¹ ; Bopeng Rao ²

¹ Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 729-737.

Résumé

We show that a Kalman rank condition is necessary and sufficient for the uniqueness of solution to a system of wave equations associated with incomplete internal observation without any restriction neither on the controlled subregion nor on the coupling matrices. The obtained result can be applied to the approximate internal controllability of the corresponding system.

Reçu le : 2021-12-14
Accepté le : 2022-01-31
Publié le : 2022-06-22

Zbl

DOI : 10.5802/crmath.341

Affiliations des auteurs :

Tatsien Li ¹ ; Bopeng Rao ²

¹ Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Tatsien Li and Bopeng Rao},
     title = {Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {729--737},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.341},
     zbl = {07547271},
     language = {en},
}

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Tatsien Li; Bopeng Rao. Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 729-737. doi : 10.5802/crmath.341. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.341/

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