Comptes Rendus
Optimal control
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.

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.

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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2018.09.006
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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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/

[1] F. Alabau-Boussouira A hierarchic multi-level energy method for the control of bidiagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls, Adv. Differ. Equ., Volume 18 (2013), pp. 1005-1072

[2] F. Ammar Khodja; A. Benabdallah; C. Dupaix Null-controllability of some reaction–diffusion systems with one control force, J. Math. Anal. Appl., Volume 320 (2006), pp. 928-944

[3] L. Hörmander Linear Partial Differential Operators, Springer-Verlag, 1976

[4] T.-T. Li; B. Rao Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math., Ser. B, Volume 34 (2013), pp. 139-160

[5] T.-T. Li; B. Rao Asymptotic controllability and asymptotic synchronization for a coupled system of wave equations with Dirichlet boundary controls, Asymptot. Anal., Volume 86 (2014), pp. 199-226

[6] T.-T. Li; B. Rao Criteria of Kalman's type to the approximate controllability and the approximate synchronization for a coupled system of wave equations with Dirichlet boundary controls, SIAM J. Control Optim., Volume 54 (2016), pp. 49-72

[7] J.-L. Lions Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, vol. 1, Masson, Paris, 1986

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