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 a three-dimensional thermoelastic body byusing time domain data is considered.The governing equation of the problem is given by a system of equations in the linear theory of thermoelasticitywhich 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.