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 *R*^{n} 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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