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Uniqueness for a boundary identification problem in thermal imaging. (English) Zbl 0911.35117

Summary: 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 \(\mathbb{R}^n\) 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.

MSC:

35R30 Inverse problems for PDEs
35K05 Heat equation
35J25 Boundary value problems for second-order elliptic equations
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