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Stabilization for the Semilinear Wave Equation in Bounded Domains

  • B. Dehman
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 46)

Abstract

The aim of this article is to prove a stabilization theorem for the semilinear wave equation on a bounded open domain of ℝ d , d ⩾ 1 with boundary Dirichlet condition. More precisely, we study systems of the type
$$ \left\{ \begin{gathered} \square u + a\left( x \right)\partial _t u + f\left( u \right) = 0 on\left] {0, + \infty } \right[x\Omega \hfill \\ u = 0 on \left] {0, + \infty } \right[ \times \partial \Omega \hfill \\ u\left( {0,x} \right) = u^0 \left( x \right) \in H_0^1 \left( \Omega \right) and \partial _t u\left( {0,x} \right) = u^1 \left( x \right) \in L^2 \left( \Omega \right) \hfill \\ \end{gathered} \right. $$
(1.1)
where the nonlinearity f satisfies some conditions which will be specified later.

Keywords

Principal Symbol Unique Continuation Carleman Estimate Geometric Control Subcritical Case 
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

  • B. Dehman
    • 1
  1. 1.Faculté des Sciences de TunisCampus Univ.TunisTunisia

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