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.
Copyright © 1998 Southwest Texas State University and University of North Texas. This article first appeared in Electronic Journal of Differential Equations, Conference 01 C-1 (1997): 23-39
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Bryan, Kurt, and Lester F. Caudill, Jr. "Uniqueness for a Boundary Identification Problem in Thermal Imaging." Electronic Journal of Differential Equations, Conference 01 C-1 (1997): 23-39.