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Spatial Behavior of Solutions in Linear Thermoelasticity with Voids and Three Delay Times

Author

Listed:
  • Manuela Carini

    (DIAM (Department of Environmental Engineering), University of Calabria, via Pietro Bucci, 87036 Arcavacata di Rende, Italy)

  • Vittorio Zampoli

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

Abstract

This brief contribution aims to complement a study of well-posedness started by the same authors in 2020, showing—for that same mathematical model—the existence of a domain of influence of external data. The object of investigation, we recall, is a linear thermoelastic model with a porous matrix modeled on the basis of the Cowin–Nunziato theory, and for which the heat exchange phenomena are intended to obey a time-differential heat transfer law with three delay times. We therefore consider, without reporting it explicitly, the (suitably adapted) initial-boundary value problem formulated at that time, as well as some analytical techniques employed to handle it in order to address the uniqueness and continuous dependence questions. Here, a domain of influence theorem is proven, showing the spatial behavior of the solution in a cylindrical domain, by activating the hypotheses that make the model thermodynamically consistent. The theorem, in detail, demonstrates that for a finite time t > 0 , the assigned external (thermomechanical) actions generate no disturbance outside a bounded domain contained within the cylindrical region of interest. The length of the work is deliberately kept to a minimum, having opted where possible for bibliographic citations in favor of greater reading fluency.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4195-:d:1255365
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    References listed on IDEAS

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    1. 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.
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