A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions

TL;DR

This paper develops a comprehensive model for heat generation in piezoelectric materials caused by acoustic waves, incorporating temperature-dependent elastic properties and establishing global solutions without smallness constraints.

Contribution

It introduces a novel thermoviscoelastic model with temperature-dependent parameters and proves global existence of solutions under mild assumptions, advancing understanding of heat generation in piezoelectric materials.

Findings

Global existence of solutions established

Model accounts for temperature-dependent elastic parameters

No smallness condition required for initial data

Abstract

A model for the generation of heat due to mechanical losses during acoustic wave propagation in a solid is considered in a Kelvin-Voigt type framework. In contrast to previous studies on related thermoviscoelastic models, in line with recent experimental findings the present manuscript focuses on situations in which elastic parameters depend on temperature. Despite an apparent loss of mathematically favorable structural properties thereby encountered, in the framework of a suitably generalized concept of solvability a result on global existence of solutions is derived under mild assumptions which, in particular, do not involve any smallness condition on the initial data.