On Wellposedness for Some Thermo-Piezo-Electric Coupling Models

TL;DR

This paper investigates the mathematical well-posedness of various thermo-piezo-electric models, including magneto-electro-thermo-elastic and quasi-electrostatic cases, to support sensor design in high-temperature environments.

Contribution

It establishes the well-posedness of a broad class of thermo-piezo-electric models, extending the theoretical foundation for sensor design and inverse problem analysis.

Findings

Proves well-posedness for magneto-electro-thermo-elastic models.

Demonstrates well-posedness of quasi-electrostatic models.

Supports design of piezoelectric sensors in high-temperature environments.

Abstract

There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well-posedness of such models. There is a need to extend the use of such sensors into high temperature environments and so this paper shows, for a broad class of models, the well-posedness of the magneto-electro-thermo-elastic problem. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case