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

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