Comparing Laplace and Helmholtz approaches to identify the rear-surface profile of a plate by means of periodic thermal data

Here we give mathematical support to the choice of the Helmholtz versus the Laplace equation for the formulation of an inverse problem in infrared thermography. Such a choice accounts for the values of physical parameters like the thermal conductivity and the Biot number. We check the effectiveness of the corresponding boundary value problems and compare the condition numbers. The Helmholtz choice is confirmed to be usually better, but there are cases in which Laplace (less expensive) works well.