Saint-Venant's principle in dynamical porous thermoelastic media with memory for heat flux

TL;DR

This paper investigates the spatial behavior and decay properties of thermoelastic porous materials with heat flux memory, establishing influence domains, decay estimates, and a uniqueness theorem without assumptions at infinity.

Contribution

It introduces a new thermodynamic framework for porous thermoelastic materials with heat flux memory and proves key properties like influence domains and decay estimates.

Findings

Established the domain of influence theorem.

Derived spatial decay estimates for the model.

Proved a uniqueness theorem for finite and infinite bodies.

Abstract

In the present paper, we study a linear thermoelastic porous material with a constitutive equation for heat flux with memory. An approximated theory of thermodynamics is presented for this model and a maximal pseudo free energy is determined. We use this energy to study the spatial behaviour of the thermodynamic processes in porous materials. We obtain the domain of influence theorem and establish the spatial decay estimates inside of the domain of influence. Further, we prove a uniqueness theorem valid for finite or infinite body. The body is free of any kind of a priori assumptions concerning the behaviour of solutions at infinity.