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

    Fingerprint

    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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