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

Manuela Carini () and Vittorio Zampoli
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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

Mathematics, 2023, vol. 11, issue 19, 1-10

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.

Keywords: linear thermoelasticity; voids; delay times; domain of influence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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