A Note on a Two-Temperature Model in Linear Thermoelasticity

TL;DR

This paper analyzes the two-temperature model in linear thermoelasticity, providing a Hilbert space framework for well-posedness, and introduces alternative models using abstract ODEs for improved understanding and potential applications.

Contribution

It offers a rigorous mathematical framework for the two-temperature model and proposes new abstract ODE-based models for better analysis and potential extensions.

Findings

Established well-posedness within a Hilbert space framework

Presented an alternative model as an abstract ODE

Highlighted potential for independent interest in alternative formulations

Abstract

We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ode. Following this line of reasoning, we propose another model being entirely an abstract ode. We highlight also an alternative way for a two-temperature model, which might be of independent interest.