Article Contents
Article Contents

# Generalized exact boundary synchronization for a coupled system of wave equations

• By means of Moore-Penrose generalized inverse, a general framework is presented to treat the generalized exact boundary synchronization for a coupled systems of wave equations.
Mathematics Subject Classification: 93B05, 93B07.

 Citation:

•  [1] A. Ben-Israel and T. N. E. Greville, Generalized Inverses. Theory and Applications, 2nd Edition, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, Springer-Verlag, New York, 2003. [2] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd Edition, Cambridge University Press, Cambridge, 2013. [3] Long Hu, Fanqiong Ji and Ke Wang, Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations, Chin. Ann. Math. Ser. B, 34 (2013), 479-490.doi: 10.1007/s11401-013-0785-9. [4] Long Hu, Tatsien Li and Bopeng Rao, Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type, Communications on Pure and Applied Analysis, 13 (2014). DOI: 10.3934/cpaa.2014.13 [5] Tatsien Li, Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Series on Applied Mathematics, 3, American Institute of Mathematical Sciences (AIMS), Springfield, MO; Higher Education Press, Beijing, 2010. [6] Tatsien Li and Bopeng Rao, Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chin. Ann. Math. Ser. B, 31 (2010), 723-742.doi: 10.1007/s11401-010-0600-9. [7] Tatsien Li and Bopeng Rao, Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls, Chin. Ann. Math. Ser. B, 34 (2013), 139-160.doi: 10.1007/s11401-012-0754-8. [8] Tatsien Li and Bopeng Rao, A note on the exact synchronization by groups for a coupled system of wave equations, to appear in Math. Meth. Appl. Sci. [9] Tatsien Li, Bopeng Rao and Long Hu, Exact boundary synchronization for a coupled system of 1-D wave equations, to appear in ESAIM: COCV. DOI: 10.1051/COCV/2013066 [10] J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués, Vol. 1, Masson, 1988. [11] J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Review, 30 (1988), 1-68.doi: 10.1137/1030001. [12] D. L. Russell, Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions, SIAM Review, 20 (1978), 639-739.doi: 10.1137/1020095.