Free Access
Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S7
Number of page(s) 29
DOI https://doi.org/10.1051/cocv/2020047
Published online 01 March 2021
  1. F. Alabau-Boussouira, Indirect boundary stabilization of weakly coupled hyperbolic systems. SIAM J. Control Optim. 2 (2002) 511–541. [Google Scholar]
  2. P. Grisvard, Elliptic Problems in Nonsmooth Domains, In Vol. 24 of Monograph and Studies in Math. Pitman, London (1985). [Google Scholar]
  3. L. Hu, T. Li and B. Rao, Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type. Commun. Pure Appl. Anal. 13 (2014) 881–901. [Google Scholar]
  4. C. Huygens, Œuvres Complètes, Vol. 15. Swets & Zeitlinger, Amsterdam (1967). [Google Scholar]
  5. I. Lasiecka and R. Triggiani, A cosine operator approach to modeling L2(0, T; L2(Γ))-boundary input hyperbolic equations. Appl. Math. Optim. 7 (1981) 35–83. [Google Scholar]
  6. I. Lasiecka and R. Triggiani, Regularity theory of hyperbolic equaitons with non-homogeneous Neumann boundary conditions. II. General boundary data. J. Differ. Equ. 94 (1991) 112–164. [Google Scholar]
  7. I. Lasiecka and R. Triggiani, recent advances in regularity of second-order hyperbolic mixed problems, and Applications. Vol. 3 of Dynamics Reported (Expositions in Dynamical Systems), edited by C.K.R.T. Jones, U. Kirchgraber, H.O. Walther. Springer, Berlin, Heidelberg (1994).. [Google Scholar]
  8. T. Li, Controllability and observability for quasilinear hyperbolic systems. AIMS Series on Applied Mathematics, Vol. 3. American Institute of Mathematical Sciences & Higher Education Press (2010). [CrossRef] [Google Scholar]
  9. T. Li, X. Lu and B. Rao, Exact boundary synchronization for a coupled system of wave equations with Neumann boundary controls. Chin. Ann. Math. 2 (2018) 233–252. [Google Scholar]
  10. T. Li, X. Lu and B. Rao, Approximate boundary null controllability and approximate boundary synchronization for a coupled system of wave equations with Neumann boundary controls. Vol. 2 of Contemporary Computational Mathematics — a Celebration of the 80th Birthday of Ian Sloan, edited by J. Dick, F. Y. Kuo, H. Woźniakowski. Springer-Verlag (2018) 837–868. [Google Scholar]
  11. T. Li and B. Rao, Synchronisation exacte d’un système couplé d’équations des ondes par des contrôles frontières de Dirichlet. C. R. Math. Acad. Sci. Paris 15–16 (2012) 767–772. [Google Scholar]
  12. T. Li and B. Rao, Exact synchronization for a coupled system of wave equation with Dirichlet boundary controls. Chin. Ann. Math. 34B (2013) 139–160. [Google Scholar]
  13. T. Li and B. Rao, Asymptotic controllability and asymptotic synchronization for a coupled system of wave equations with Dirichlet boundary controls. Asymp. Anal. 86 (2014) 199–226. [Google Scholar]
  14. T. Li and B. Rao, A note on the exact synchronization by groups for a coupled system of wave equations. Math. Meth. Appl. Sci. 13 (2015) 2803–2808. [Google Scholar]
  15. T. Li and B. Rao, On the exactly synchronizable state to a coupled system of wave equations. Portugaliae Math. 72 (2015) 83–100. [Google Scholar]
  16. T. Li and 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. 1 (2016) 49–72. [Google Scholar]
  17. T. Li and B. Rao, Exact synchronization by groups for a coupled system of wave equations with Dirichlet boundary controls. J. Math. Pures Appl. 1 (2016) 86–101. [Google Scholar]
  18. T. Li and B. Rao, Exact boundary controllability for a coupled system of wave equations with Neumann controls. Chin. Ann. Math. 38B (2017) 473–488. [Google Scholar]
  19. T. Li and B. Rao, On the approximate boundary synchronization for a coupled system of wave equations: Direct and indirect boundary controls. ESAIM: COCV 24 (2019) 1675–1704. [Google Scholar]
  20. T. Li, B. Rao and L. Hu, Exact boundary synchronization for a coupled system of 1-D wave equations. ESAIM: COCV 20 (2014) 339–361. [CrossRef] [EDP Sciences] [Google Scholar]
  21. T. Li, B. Rao and Y. Wei, Generalized exact boundary synchronization for a coupled system of wave equations. Discrete Contin. Dyn. Syst. 34 (2014) 2893–2905. [Google Scholar]
  22. J.-L. Lions, Equations Différentielles Opérationnelles et Problèmes aux Limites. Grundlehren Vol. 111. Berlin/ Göttingen/Heidelberg, Springer (1961). [Google Scholar]
  23. J.-L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Gauthier-Villars, Paris (1969). [Google Scholar]
  24. J.-L. Lions, Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués. Vol. 1 Masson, Paris (1988). [Google Scholar]
  25. Z. Liu, Songmu Zheng, Semigroups Associated with Dissipative Systems. Vol. 398 CRC Press (1999). [Google Scholar]
  26. X. Lu, Controllability of classical solutions implies controllability of weak solutions for a coupled system of wave equations and its applications. Math. Meth. Appl. Sci. 4 (2016) 709–721. [Google Scholar]
  27. X. Lu, Exact boundary controllability and exact boundary synchronization for a coupled system of wave equations with Neumann and coupled Robin boundary controls. Ph.D. thesis, Université de Strasbourg, France (2018). [Google Scholar]
  28. J. Simon, Compact sets in the space Lp(0, T; B). Ann. Mat. Pura Appl. 146 (1986) 65–96. [Google Scholar]
  29. N. Wiener, Cybernetics, or Control and Communication in the Animal and the Machine, 2nd ed. MIT Press, Cambridge USA (1967). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.