Bryan, Kurt; Caudill, Lester F. jun. Uniqueness for a boundary identification problem in thermal imaging. (English) Zbl 0911.35117 Electron. J. Differ. Equ. 1997, Conf. 01, 23-39 (1997). 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. Cited in 12 Documents MSC: 35R30 Inverse problems for PDEs 35K05 Heat equation 35J25 Boundary value problems for second-order elliptic equations Keywords:non-destructive testing; thermal imaging; unknown portion of the boundary; Cauchy data; eigenfunction expansions; uniqueness PDFBibTeX XMLCite \textit{K. Bryan} and \textit{L. F. Caudill jun.}, Electron. J. Differ. Equ. 1997, 23--39 (1997; Zbl 0911.35117) Full Text: EuDML EMIS