Backward in time problem of a double porosity material with microtemperature

TL;DR

This paper investigates the backward in time problem for double porosity thermoelastic materials with microtemperature, establishing uniqueness and non-localization results in bounded and semi-infinite domains.

Contribution

It introduces new theoretical results on the impossibility of time localization and the Phragmen-Lindelof alternative for such materials.

Findings

Proves non-localization of solutions in bounded domains.

Establishes uniqueness for the backward in time problem.

Derives Phragmen-Lindelof alternative in semi-infinite cylinders.

Abstract

In the present study we consider the theory of thermoelastodynamics in the case of materials with double porosity structure and microtemperature. This study is devoted to the investigation of a backward in time problem associated with double porous thermoelastic materials with microtemperature. In the first part of the paper, in case of the bounded domains the impossibility of time localization of solutions is obtained. This study is equivalent to the uniqueness of solutions for the backward in time problem. In the second part of the paper, a Phragmen-Lindelof alternative in the case of semi-infinite cylinders is obtained.