Asymptotic behavior of a delayed wave equation without displacement term

Kaïs Ammari*, Boumediène Chentouf

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number117
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume68
Issue number5
DOIs
Publication statusPublished - Oct 1 2017
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Logarithmic stability
  • Time-delay
  • Wave equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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