We discuss inverse problems of boundary determination for
parabolic initial-boundary value problems. In this setting, the
desired unknown is a portion of the boundary of the spatial
domain. This unknown is to be determined from a single Cauchy
data pair prescribed on another portion of the boundary. This
type of inverse problem models the use of thermal methods in
nondestructive damage assessment. This specific problem could
represent a model of thermal imaging, in which an inaccessible
portion of the boundary of a sample is to be estimated by
temperature measurements (resulting from an induced heat flux
pattern) taken on another portion of the boundary.
We discuss uniqueness for this inverse problem, and important
stability issues. We present a numerical algorithm designed to
produce stable and reliable approximate solutions to this
problem. We also discuss a number of important and interesting
issues, both of a theoretical and practical nature, that arise in
the study of this inverse problem.
Copyright. All Rights Reserved.