On Boundary Control Problems in Slow Processes for Piezothermoelastic Plates

TL;DR

This paper investigates boundary control in slow processes of piezothermoelastic plates, demonstrating how temperature can be regulated via electric potential differences under specific boundary conditions.

Contribution

It introduces a boundary control approach for piezothermoelastic plates with slow boundary variations, highlighting the role of electric potential in temperature regulation.

Findings

Temperature control is achievable through electric potential differences.

Boundary conditions significantly influence thermal response.

The study applies to materials with hexagonal crystal symmetry.

Abstract

We consider a piezothermoelastic panel occupied by a material of hexagonal crystal class. We study the response when the boundary conditions vary very slowly with time and one of the bounding faces is subject to thermal exposure. We show that in some cases the temperature on the other bounding face can be controlled by the difference of electric potential between the faces.