A thermoelastic theory with microtemperatures of type III

TL;DR

This paper develops a nonlinear thermoelasticity theory incorporating microtemperatures of type III, allowing finite-speed wave propagation with energy dissipation, and analyzes its mathematical properties and solution behavior.

Contribution

It introduces a new nonlinear thermoelasticity model with microtemperatures of type III based on Green-Naghdi theory, including linearization, well-posedness, and asymptotic analysis.

Findings

Finite-speed propagation of thermal and microtemperature waves.

Linearized equations are well-posed in anisotropic media.

Solutions cannot be localized in time, indicating persistent wave effects.

Abstract

In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a nonlinear theory of thermoelasticity with microtemperatures of type III. This theory permits propagation of both thermal and microtemperatures waves at finite speeds with dissipation of energy. The equations of the linear theory are also obtained. With the help of the semigroup theory of linear operators we establish that the linear anisotropic problem is well posed and we study the asymptotic behavior of the solutions. Finally, we investigate the impossibility of the localization in time of solutions.