Determination of generalized exact boundary synchronization matrix for a coupled system of wave equations

Abstract

For a coupled system of wave equations with Dirichlet boundary controls, this paper deals with the possible choice of its generalized synchronization matrices so that the admissible generalized exact boundary synchronizations for this system are obtained.

Keywords

Coupled system of wave equations / generalized exact boundary synchronization / generalized synchronization matrix

References

[1] Gohberg I, Lancaster P, Rodman L. Invariant Subspaces of Matrices with Applications. New York: John Wiley & Sons, Inc, 1986

[2] Li T T, Rao B P. Synchronisation exacte d’un système couplé d’équations des ondes par des contrôles frontières de Dirichlet. C R Math Acad Sci Paris, 2012, 350(15-16): 767–772

[3] Li T T, Rao B P. Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls. Chin Ann Math Ser B, 2013, 34(1): 139–160

[4] Li T T, Rao B P. A note on the exact synchronization by groups for a coupled system of wave equations. Math Methods Appl Sci, 2015, 38(2): 241–246

[5] Li T T, Rao B P. On the exactly synchronizable state to a coupled system of wave equations. Port Math, 2015, 72(2-3): 83–100

[6] Li T T, Rao B P. Exact synchronization by groups for a coupled system of wave equations with Dirichlet boundary controls. J Math Pures Appl (9), 2016, 105(1): 86–101

[7] Li T T, Rao B P, Hu L. Exact boundary synchronization for a coupled system of 1-D wave equations. ESAIM Control Optim Calc Var, 2014, 20(2): 339–361

[8] Li T T, Rao B P, Wei Y M. Generalized exact boundary synchronization for a coupled system of wave equations. Discrete Contin Dyn Syst, 2014, 34(7): 2893–2905

[9] Lions J L. Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués. Tome 1. Paris: Masson, 1988

[10] Wang Y Y. Generalized exact boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. Chin Ann Math Ser B (to appear)

[11] Wang Y Y. On the generalized exact boundary synchronization for a coupled system of wave equations. Math Methods Appl Sci (to appear)

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