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Stabilization for the Wave Equation on Exterior Domains

  • L. Aloui
  • M. Khenissi
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 46)

Abstract

The aim of this article is the study of stabilization for the wave equation on exterior domains, with Dirichlet boundary condition. More precisely, let O be a bounded, smooth domain of ℝ n (n odd); we consider the following wave equation on Ω = c Ō:
$$ \left( E \right)\left\{ \begin{gathered} \square u = \partial _t^2 u = 0 on \mathbb{R} \times \Omega \hfill \\ u\left( 0 \right) = f_1 ,\partial _t u\left( 0 \right) = f_2 on \Omega \hfill \\ u_{\partial \Omega \times \mathbb{R}} = 0 \hfill \\ \end{gathered} \right. $$
with the initial data f = (f 1, f 2) ∈ H(Ω) = H D × L 2, the completion of (C 0 (Ω))2 for the energy norm.

Keywords

Wave Equation Exponential Decay Exterior Domain Finite Dimensional Space Carleman Estimate 
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.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • L. Aloui
    • 1
  • M. Khenissi
    • 1
  1. 1.Département de Mathématiques et InformatiqueFaculté des Sciences de GabèsGabèsTunisia

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