Uniqueness for a boundary identification problem in thermal imaging

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 ${mathbb R}^n$ 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.

Keywords

• Inverse problems
• non-destructive testing
• thermal imaging.