We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region Ω from measurements of the Cauchy data for solutions to the heat equation on Ω. By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.
Copyright © 1998 IOP Publishing. Article first published online: DEC 1998. DOI: doi:10.1088/0266-5611/14/6/005.
The definitive version is available at:
Bryan, Kurt, and Lester F. Caudill. "Stability and Reconstruction for an Inverse Problem for the Heat Equation." Inverse Problems 14, no. 6 (December 1998): 1429-453. doi:10.1088/0266-5611/14/6/005.
Bryan, Kurt and Caudill, Lester, "Stability and Reconstruction for an Inverse Problem for the Heat Equation" (1998). Math and Computer Science Faculty Publications. 98.