Solving elliptic Cauchy problems and the identification of nonlinear corrosion

Authors:
Giovanni Alessandrini;Eva Sincich
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Italy;S.I.S.S.A., Trieste, Italy
Venue:
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Year:
2007

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Abstract

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.