Differential Equations and Computational Simulations III
J. Graef, R. Shivaji, B. Soni J. & Zhu (Editors)
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 23-39.

Uniqueness for a boundary identification problem in thermal imaging

Kurt Bryan & Lester F. Caudill, Jr.

Abstract:
An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in Rn from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs.

Published November 12, 1998.
Mathematics Subject Classifications: 35A40, 35J25, 35R30.
Key words and phrases: Inverse problems, non-destructive testing, thermal imaging.

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Kurt Bryan
Department of Mathematics
Rose-Hulman Institute of Technology
Terre Haute, IN 47803, USA.
E-mail address: kurt.bryan@rose-hulman.edu

Lester F. Caudill, Jr.
Department of Mathematics and Computer Science
University of Richmond
Richmond, VA 23173, USA
E-mail address: lcaudill@richmond.edu

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