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On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity

Author

Listed:
  • Manuela Carini

    (Department of Environmental Engineering, University of Calabria, DIAm, via Pietro Bucci 42/B, 87036 Arcavacata di Rende (CS), Italy)

  • Vittorio Zampoli

    (Department of Information and Electrical Engineering and Applied Mathematics, University of Salerno, DIEM, via Giovanni Paolo II, 84084 Fisciano (SA), Italy)

Abstract

Through the present work, we want to lay the foundation of the well-posedness question for a linear model of thermoelasticity here proposed, in which the presence of voids into the elastic matrix is taken into account following the Cowin–Nunziato theory, and whose thermal response obeys a three-phase lag time-differential heat transfer law. By virtue of the linearity of the model investigated, the basic initial-boundary value problem is conveniently modified into an auxiliary one; attention is paid to the uniqueness question, which is addressed through two alternative paths, i.e., the Lagrange identity and the logarithmic convexity methods, as well as to the continuous dependence issue. The results are achieved under very weak assumptions involving constitutive coefficients and delay times, at most coincident with those able to guarantee the thermodynamic consistency of the model.

Suggested Citation

  • Manuela Carini & Vittorio Zampoli, 2020. "On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:371-:d:329631
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    References listed on IDEAS

    as
    1. Vittorio Zampoli, 2019. "On the Increase in Signal Depth due to High-Order Effects in Micro- and Nanosized Deformable Conductors," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-11, January.
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    Citations

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    Cited by:

    1. Sayed M. Abo-Dahab & Alaa A. El-Bary & Yas Al-Hadeethi & Mohamed Alkashif, 2020. "Mathematical Model on Gravitational Electro-Magneto-Thermoelasticity with Two Temperature and Initial Stress in the Context of Three Theories," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    2. Manuela Carini & Vittorio Zampoli, 2023. "Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times," Mathematics, MDPI, vol. 11(19), pages 1-10, October.
    3. Tareq Saeed & Ibrahim A. Abbas, 2021. "The Effect of Fractional Time Derivative on Two-Dimension Porous Materials Due to Pulse Heat Flux," Mathematics, MDPI, vol. 9(3), pages 1-14, January.

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