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.
