Kalman's criterion on the uniqueness of continuation for the nilpotent system of wave equations

Tatsien Li; Bopeng Rao

doi:10.1016/j.crma.2018.09.006

Optimal control

Kalman's criterion on the uniqueness of continuation for the nilpotent system of wave equations
[Critère de Kalman sur l'unicité de la continuation pour le système nilpotent d'équations des ondes]

Présenté par : Philippe G. Ciarlet

Tatsien Li ^1,^2,³ ; Bopeng Rao ^1,⁴

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Shanghai Key Laboratory for Contemporary Applied Mathematics, Shanghai, China
³ Nonlinear Mathematical Modeling and Methods Laboratory, Shanghai, China
⁴ Institut de recherche mathématique avancée, Université de Strasbourg, 67084 Strasbourg, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1188-1194.

Résumé
Abstract

Dans cette Note, nous considérons un système d'équations des ondes couplées par une matrice nilpotente avec la condition aux limites homogène de Dirichlet. Nous établissons l'unicité de la solution si l'observation partielle de Neumann satisfait le critère de Kalman.

In this Note, we consider a system of wave equations coupled by a nilpotent matrix with homogeneous Dirichlet boundary condition. We establish the uniqueness of the solution when partial Neumann observation satisfies Kalman's rank condition.

Reçu le : 2018-08-04
Accepté le : 2018-09-02
Publié le : 2018-10-02

DOI : 10.1016/j.crma.2018.09.006

Affiliations des auteurs :

Tatsien Li ^{1, 2, 3} ; Bopeng Rao ^{1, 4}

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Shanghai Key Laboratory for Contemporary Applied Mathematics, Shanghai, China
³ Nonlinear Mathematical Modeling and Methods Laboratory, Shanghai, China
⁴ Institut de recherche mathématique avancée, Université de Strasbourg, 67084 Strasbourg, France

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     title = {Kalman's criterion on the uniqueness of continuation for the nilpotent system of wave equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1188--1194},
     publisher = {Elsevier},
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     year = {2018},
     doi = {10.1016/j.crma.2018.09.006},
     language = {en},
}

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Tatsien Li; Bopeng Rao. Kalman's criterion on the uniqueness of continuation for the nilpotent system of wave equations. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1188-1194. doi : 10.1016/j.crma.2018.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.09.006/

Bibliographie
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Tatsien Li; Bopeng Rao Approximate internal controllability and synchronization of a coupled system of wave equations, European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations, Volume 30 (2024), p. 21 (Id/No 1) | DOI:10.1051/cocv/2023008 | Zbl:1532.93022
Tatsien Li; Bopeng Rao Approximate Internal Controllability, Synchronization for Wave Equations with Locally Distributed Controls, Volume 5 (2024), p. 15 | DOI:10.1007/978-981-97-0992-2_3
Tatsien Li; Bopeng Rao Exactly synchronizable state and approximate controllability for a coupled system of wave equations with locally distributed controls, SIAM Journal on Control and Optimization, Volume 61 (2023) no. 3, pp. 1460-1471 | DOI:10.1137/22m1488430 | Zbl:1519.93033
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. Académie des Sciences, Paris, Volume 360 (2022), pp. 729-737 | DOI:10.5802/crmath.341 | Zbl:1497.93020
Yanyan Wang Generalized approximate boundary synchronization for a coupled system of wave equations, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 7, pp. 5309-5325 | DOI:10.1002/mma.7111 | Zbl:1471.35196
Tatsien Li; Bopeng Rao Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems, European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations, Volume 26 (2020), p. 26 (Id/No 117) | DOI:10.1051/cocv/2020062 | Zbl:1461.93416

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