On the identification and reconstruction of sources in a potential problem from boundary

In this talk we address the question of identifying a source function from boundary measurements, for the Laplace equation. This is an inverse problem that models (among others) the reconstruction of heat sources from boundary measurements of temperature and heat flux, in linear diffusion problems. It is a well known inverse problem that lacks uniqueness and some extra information concerning the source must be considered. One way is to consider intrusive measurements (knowledge of the source at some domain points). In non-intrusive evaluation (which is the approach of this work) the extra source information is an indirect one. We present several classes where this indirect information is sufficient to obtain uniqueness and show how to recover the harmonic part of a source from the boundary data. In particular, a one to one relation between the Cauchy data and the harmonic part of the source is established. Several numerical simulations will be presented. This is an joint work that results from a cooperation between engineering and mathematics departments of UFRJ (Brazil) and IST.