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On the existence and uniqueness in phase-lag thermoelasticity

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Abstract

This paper is devoted to analyze the phase-lag thermoelasticity problem. We study two different cases and we prove, for each one of them, that the solutions of the problem are determined by a quasi-contractive semigroup. As a consequence, existence, uniqueness and continuous dependence of the solutions are obtained.

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Notes

  1. Here and from now on, \(g^{(k)}\) denotes the k-th derivative of the function g with respect to the time and, in particular, \(g^{(0)}=g.\)

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Acknowledgements

Investigations reported in this paper were supported by projects “Análisis Matemático de las Ecuaciones en Derivadas Parciales de la Termomecánica” (MTM2013-42004-P, AEI/FEDER, UE) and “Análisis Matemático de Problemas de la Termomecánica” (MTM2016-74934-P, AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. The authors want to thank an anonymous referee for his useful comments.

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  1. Departament de Matemàtiques, UPC, C. Colom 11, 08222, Terrassa, Barcelona, Spain

    Antonio Magaña & Ramón Quintanilla

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  1. Antonio Magaña
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  2. Ramón Quintanilla
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Correspondence to Antonio Magaña.

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Magaña, A., Quintanilla, R. On the existence and uniqueness in phase-lag thermoelasticity. Meccanica 53, 125–134 (2018). https://doi.org/10.1007/s11012-017-0727-9

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  • DOI: https://doi.org/10.1007/s11012-017-0727-9

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