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

摘要

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