Free Access
Issue
ESAIM: COCV
Volume 14, Number 3, July-September 2008
Page(s) 604 - 631
DOI https://doi.org/10.1051/cocv:2007062
Published online 21 December 2007
  1. C. Castro and S. Micu, Boundary controllability of a linear semi-discrete 1D wave equation derived from a mixed finite element method. Numer. Math. 102 (2006) 413–462. [CrossRef] [MathSciNet]
  2. R. Glowinski, C.H. Li and J.-L. Lions, A numerical approach to the exact boundary controllability of the wave equation (I), Dirichlet controls: Description of the numerical methods. Japan. J. Appl. Math. 7 (1990) 1–76. [CrossRef] [MathSciNet]
  3. A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. J. Math. Pures Appl. 68 (1989) 457–465. [MathSciNet]
  4. L. Ignat, Propiedades cualitativas de esquemas numéricos de aproximción de ecuaciones de difusión y de dispersión. Ph.D. thesis, Universidad Autónoma de Madrid, Spain (2006).
  5. J.A. Infante and E. Zuazua, Boundary observability for the space discretization of the 1D wave equation. ESAIM: M2AN 33 (1999) 407–438. [CrossRef] [EDP Sciences] [MathSciNet]
  6. A.E. Ingham, Some trigonometrical inequalities with applications in the theory of series. Math. Z. 41 (1936) 367–379. [CrossRef] [MathSciNet]
  7. V. Komornik, Exact Controllability and Stabilization. The Multiplier Method. Wiley, Chichester; Masson, Paris (1994).
  8. V. Komornik and P. Loreti, Fourier Series in Control Theory, Springer Monographs in Mathematics. Springer-Verlag, New York (2005).
  9. J.-L. Lions, Contrôlabilité Exacte, Stabilisation et Perturbation de Systèmes Distribués. Tome 1. Contrôlabilité Exacte. Masson, Paris, RMA 8 (1988).
  10. P. Loreti and V. Valente, Partial exact controllability for spherical membranes. SIAM J. Control Optim. 35 (1997) 641–653. [CrossRef] [MathSciNet]
  11. S. Micu, Uniform boundary controllability of a semi-discrete 1D wave equation. Numer. Math. 91 (2002) 723–766. [CrossRef] [MathSciNet]
  12. S. Micu and E. Zuazua, Boundary controllability of a linear hybrid system arising in the control of noise. SIAM J. Cont. Optim. 35 (1997) 1614–1638. [CrossRef] [MathSciNet]
  13. A. Münch, Family of implicit and controllable schemes for the 1D wave equation. C. R. Acad. Sci. Paris Sér. I 339 (2004) 733–738.
  14. M. Negreanu, Numerical methods for the analysis of the propagation, observation and control of waves. Ph.D. thesis, Universidad Complutense Madrid, Spain (2003). Available at http://www.uam.es/proyectosinv/cen/indocumentos.html
  15. M. Negreanu and E. Zuazua, Convergence of a multigrid method for the controllability of a 1D wave equation. C. R. Acad. Sci. Paris, Sér. I 338 (2004) 413–418.
  16. M. Negreanu and E. Zuazua, Discrete Ingham inequalities and applications. SIAM J. Numer. Anal. 44 (2006) 412–448. [CrossRef] [MathSciNet]
  17. E. Zuazua, Propagation, observation, control and numerical approximation of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet]
  18. E. Zuazua, Control and numerical approximation of the wave and heat equations, in Proceedings of the ICM 2006, Vol. III, “Invited Lectures", European Mathematical Society Publishing House, M. Sanz-Solé et al. Eds. (2006) 1389–1417.

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.