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Stability of thermoelastic Bresse systems

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Abstract

In this paper, we study thermoelastic Bresse systems where the heat conductions, acting on the axial force, are modeled for both Fourier’s and Cattaneo’s laws. For the Fourier’s case, we prove exponential stability of solutions if and only if the condition of equal wave speeds is satisfied. For the Cattaneo’s case, we characterize the exponential stability by a new condition on the coefficients of the system. We also prove, in the general case, polynomial stability of solutions. These results complement previous results obtained by Liu and Rao (Z Angew Math Phys 60:54–69, 2009), Fatori and Rivera (IMA J Appl Math 75:881–904, 2010) and Dell’Oro (J Differ Equ 258:3902–3927, 2015).

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Acknowledgements

The authors are indebted to the anonymous referees for their useful suggestions which helped to improve the earlier version of the manuscript.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Ilha do Fundão, Rio de Janeiro, RJ , CEP 21945-970, Brazil

    Pedro Roberto de Lima

  2. Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG , CEP 36036-900, Brazil

    Hugo D. Fernández Sare

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  1. Pedro Roberto de Lima
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  2. Hugo D. Fernández Sare
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Correspondence to Pedro Roberto de Lima.

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P. R. de Lima is supported by Capes.

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de Lima, P.R., Fernández Sare, H.D. Stability of thermoelastic Bresse systems. Z. Angew. Math. Phys. 70, 3 (2019). https://doi.org/10.1007/s00033-018-1057-z

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  • DOI: https://doi.org/10.1007/s00033-018-1057-z

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