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Article Dans Une Revue Zeitschrift für Angewandte Mathematik und Physik Année : 2017

Asymptotic behavior of a delayed wave equation without displacement term

Boumediene Chentouf
  • Fonction : Auteur

Résumé

This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any displacement term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter, LaSalle's invariance principle is invoked in order to establish the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data. More importantly, without any geometric condition such as BLR condition (Bardos et al. in SIAM J Control Optim 30 1024-1064, 1992; Lebeau and Robbiano in Duke Math J 86 465-491, 1997) in the control zone, the logarithmic convergence is proved by using an interpolation inequality combined with a resolvent method.

Dates et versions

hal-02169458 , version 1 (01-07-2019)

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Citer

Kaïs Ammari, Boumediene Chentouf. Asymptotic behavior of a delayed wave equation without displacement term. Zeitschrift für Angewandte Mathematik und Physik, 2017, 68 (5), ⟨10.1007/s00033-017-0865-x⟩. ⟨hal-02169458⟩
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