An inverse problem for a parabolic 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 Dirichlet data on a known portion of the boundary. It is shown that under reasonable hypotheses uniqueness results hold.
Bryan, Kurt M. and Caudill, Lester F., "Uniqueness for a Boundary Identification Problem in Thermal Imaging" (1996). Mathematical Sciences Technical Reports (MSTR). 118.