Data Recovery from Cauchy Measurements in Transient Heat Transfer (Journal of Mathematical Study, 2022)
We study the ill-posedness degree of the reconstruction processes of missing boundary data or initial states in the transient heat conduction. Both problems areseverely ill-posed. This is a powerful indicator about the way the instabilities will affect the computations in the numerical recovery methods. We provide rigorous proofsof this result where the conductivites are space dependent. The theoretical work isconcerned with the unsteady heat equation in one dimension even though most of theresults obtained here are readily extended to higher dimensions.