  We deal with an inverse problem arising in corrosion detection. The presence
of corrosion damage is modeled by a nonlinear boundary condition on the
inaccessible portion of the metal specimen. We propose a method for the
approximate reconstruction of such a nonlinearity. A crucial step of this
procedure, which encapsulates the major cause of the ill-posedness of the
problem, consists of the solution of a Cauchy problem for an elliptic equation.
For this purpose we propose an SVD approach.

Analysis of PDEs