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

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.

33 pages, corrected line 3 up on p.28 and line 2 down on page 29 which are corresponding to the correction of (A.13)

References in corpus (6)

• On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain
• The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator
• An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method
• The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain
• On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method
• A remark on finding the coefficient of the dissipative boundary condition via the enclosure method in the time domain

Cited by in corpus (7)

• Extracting discontinuity using the probe and enclosure methods
• The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell type initial data
• Prescribing a heat flux coming from a wave equation
• The enclosure method for the heat equation using time-reversal invariance for a wave equation
• Detecting a hidden obstacle via the time domain enclosure method. A scalar wave case
• Numerical Algorithms for the Reconstruction of Space-Dependent Sources in Thermoelasticity
• On finding a penetrable obstacle using a single electromagnetic wave in the time domain