# On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

## TL;DR

This paper develops a new time-domain enclosure method to detect cavities inside thermoelastic bodies using a single surface displacement measurement over time, extending classical wave equation techniques to coupled thermoelastic systems.

## Contribution

It introduces a novel enclosure method tailored for thermoelastic bodies, accommodating the coupled heat and elastic wave equations, and compares results with the decoupled case.

## Key findings

- Successfully detects cavities using a single measurement
- Extends the enclosure method to coupled thermoelastic systems
- Provides comparative analysis with decoupled models

## Abstract

A mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory of thermoelasticity which is a coupled system of the elastic wave and heat equations. A new version of the enclosure method in the time domain which is originally developed for the classical wave equation is established. For a comparison, the results in the decoupled case are also given.