Stabilization of the Wave Equation by the Boundary

  • Gilles Lebeau
  • Luc Robbiano
Conference paper
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 21)


We consider here problems of stabilization for the wave equation on a connected manifold with a compact boundary. The stabilization, i.e. the decrease in energy, will be obtained by a dissipative boundary condition.


Wave Equation Partial Differential Operator Geodesic Flow Interpolation Inequality Connected Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B.L.R]
    C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim. 30 (1992), 1024–1065.MathSciNetMATHCrossRefGoogle Scholar
  2. [Ha]
    A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations, J. Diff. Equations 59 (1985), 145–154.MathSciNetMATHCrossRefGoogle Scholar
  3. [Ho]
    L. Hörmander, The Analysis of Linear Partial Differential Operators, Springer Verlag, 1985.Google Scholar
  4. L] G. Lebeau, Equations des ondes amorties,Algebraic and Geometric Methods in Mathematical Physics, Kluwer’s Maths-Physics Book Series (to appear).Google Scholar
  5. [L.R]
    G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur, Comm. Partial Diff. Equations 20 (1995), 335–356.MathSciNetMATHGoogle Scholar
  6. [R]
    L. Robbiano, Fonction de coût et contrôle des solutions des équations hyperboliques, Asymptotic Analysis 10 (1995), 95–115.MathSciNetMATHGoogle Scholar
  7. [T]
    D. Tataru, A priori estimates of Carleman’s type in domains with boundary, J. Math. Pures et Appl. 73 (1994), 355–387.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Gilles Lebeau
    • 1
  • Luc Robbiano
    • 2
    • 3
  1. 1.Département de MathématiquesUniversité de Paris-SudOrsay CedexFrance
  2. 2.Université de Paris-Val de Marne, UFR de SciencesCréteil CedexFrance
  3. 3.Département de MathématiquesUniversité de Paris-SudOrsay CedexFrance

Personalised recommendations