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Decay of quasi-static porous-thermo-elastic waves

Abstract

We study the behavior in time of the solutions to several systems of equations for porous-thermo-elastic problems when one of the variables is considered to be quasi-static or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction models.

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Acknowledgements

Research is supported by Project Análisis Matemático de Problemas de la Termomecánica (MTM2016-74934-P, AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. It is also supported by Project Análisis Matemático Aplicado a la Termomecánica (PID2019-105118GB-I00) of the Spanish Ministry of Science, Innovation and Universities.

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Correspondence to A. Magaña.

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Magaña, A., Quintanilla, R. Decay of quasi-static porous-thermo-elastic waves. Z. Angew. Math. Phys. 72, 125 (2021). https://doi.org/10.1007/s00033-021-01557-z

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  • DOI: https://doi.org/10.1007/s00033-021-01557-z

Keywords

  • Types II/III thermo-elasticity
  • Quasi-static
  • Exponential decay

Mathematics Subject Classification

  • 74F05
  • 74H40
  • 74A60
  • 35Q74