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Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound

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Abstract

In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacements. We establish the well-posedness of the system and prove that the system is exponentially stable depending on the parameters of the system. Furthermore, we show that in general, the system is not exponential stable. In this regards, we prove that the solution decays polynomially.

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Acknowledgments

The authors thank KFUPM and UoHB for their continuous support. The third author is partially sponsored by KFUPM under Project No. IN141015.

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Authors and Affiliations

  1. Department of Mathematics, Djillali Liabes University, P. O. Box 89, Sidi Bel Abbes, 22000, Algeria

    Ahmed A. Keddi

  2. Mathematics Department, University of Hafr Al-Batin, P. O. Box 1803, Hafr Al-Batin, 31991, Saudi Arabia

    Tijani A. Apalara

  3. 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. Ahmed A. Keddi
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  2. Tijani A. Apalara
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  3. Salim A. Messaoudi
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Correspondence to Salim A. Messaoudi.

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Keddi, A.A., Apalara, T.A. & Messaoudi, S.A. Exponential and Polynomial Decay in a Thermoelastic-Bresse System with Second Sound. Appl Math Optim 77, 315–341 (2018). https://doi.org/10.1007/s00245-016-9376-y

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  • DOI: https://doi.org/10.1007/s00245-016-9376-y

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