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Existence and energy decay of a nonuniform Timoshenko system with second sound

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Abstract

In this paper, we consider a linear thermoelastic Timoshenko system with variable physical parameters, where the heat conduction is given by Cattaneo’s law and the coupling is via the displacement equation. We discuss the well-posedness and the regularity of solution using the semigroup theory. Moreover, we establish the exponential decay result provided that the stability function \(\chi _{r}(x)=0\). Otherwise, we show that the solution decays polynomially.

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Authors and Affiliations

  1. Faculty of Mathematics, AMNEDP Laboratory, USTHB, PO Box 32 , 16111, El Alia, Bab Ezzouar, Algiers, Algeria

    Taklit Hamadouche

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046 , Dhahran, 31261, Saudi Arabia

    Salim A. Messaoudi

Authors
  1. Taklit Hamadouche
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  2. Salim A. Messaoudi
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Correspondence to Salim A. Messaoudi.

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Hamadouche, T., Messaoudi, S.A. Existence and energy decay of a nonuniform Timoshenko system with second sound. Z. Angew. Math. Phys. 69, 6 (2018). https://doi.org/10.1007/s00033-017-0897-2

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  • DOI: https://doi.org/10.1007/s00033-017-0897-2

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