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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     author = {Tatsien Li and Bopeng Rao},
     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},
     volume = {356},
     number = {11-12},
     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
Cité par

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