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Bresse System in Thermoelasticity of Type III Acting on Shear Force

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Abstract

In this work we are considering the thermoelastic beam system where the oscillations are defined by the Bresse model and the heat conduction is given by Green and Naghdi theories. Our main result is to show that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal. It is worth mentioning that this theory is very new and then few applicability studies have been developed for this theory. However, mathematical and physical analysis is needed to clarify its applicability.

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Acknowledgements

I am grateful to the anonymous referees for the very careful reading and correction of various misprints. The author thanks IMPA for its hospitality during his stay as a visiting professor. The author was been partially supported by the CNPq Grant 163428/2014-0 and 302899/2015-4.

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  1. Programa de Pós-Graduação em Matemática-ICEN, Universidade Federal do Pará, Campus Universitário do Guamá, Rua Augusto Corrêa 01, Belém, Pará, Brazil

    M. L. Santos

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  1. M. L. Santos
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Santos, M.L. Bresse System in Thermoelasticity of Type III Acting on Shear Force. J Elast 125, 185–216 (2016). https://doi.org/10.1007/s10659-016-9576-3

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  • DOI: https://doi.org/10.1007/s10659-016-9576-3

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