On the stability of the Bresse system with frictional damping

Tej-eddine Ghoul, Moez Khenissi, Belkacem Said-Houari

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the Bresse system with frictional damping terms and prove some optimal decay results for the L2-norm of the solution and its higher order derivatives. In fact, if we consider just one damping term acting on the second equation of the solution, we show that the solution does not decay at all. On the other hand, by considering one damping term alone acting on the third equation, we show that this damping term is strong enough to stabilize the whole system. In this case, we found a completely new stability number that depends on the parameters in the system. In addition, we prove the optimality of the results by using eigenvalues expansions. We have also improved the result obtained recently in [12] for the two damping terms case and get better decay estimates. Our obtained results have been proved under some assumptions on the wave speeds of the three equations in the Bresse system.

Original languageEnglish (US)
Pages (from-to)1870-1898
Number of pages29
JournalJournal of Mathematical Analysis and Applications
Volume455
Issue number2
DOIs
StatePublished - Nov 15 2017

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Damping Term
Damping
Decay
Stability number
Higher order derivative
Decay Estimates
Wave Speed
Optimality
Derivatives
Eigenvalue
Norm

Keywords

  • Bresse system
  • Decay rate
  • Regularity loos
  • Timoshenko system
  • Wave speeds

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On the stability of the Bresse system with frictional damping. / Ghoul, Tej-eddine; Khenissi, Moez; Said-Houari, Belkacem.

In: Journal of Mathematical Analysis and Applications, Vol. 455, No. 2, 15.11.2017, p. 1870-1898.

Research output: Contribution to journalArticle

Ghoul, Tej-eddine ; Khenissi, Moez ; Said-Houari, Belkacem. / On the stability of the Bresse system with frictional damping. In: Journal of Mathematical Analysis and Applications. 2017 ; Vol. 455, No. 2. pp. 1870-1898.
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