Solving elliptic Cauchy problems and the identification of nonlinear corrosion

Details Solving elliptic Cauchy problems and the identification of nonlinear corrosion Solving elliptic Cauchy problems and the identification of nonlinear corrosion

2004-11-22

arxiv.org/abs/math/0411481v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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