Solving elliptic Cauchy problems and the identification of nonlinear corrosion

Giovanni Alessandrini; Eva Sincich

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Solving elliptic Cauchy problems and the identification of nonlinear corrosion

Giovanni Alessandrini·Eva Sincich

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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.

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Giovanni Alessandrini, Eva Sincich. 2004-11-22. Solving elliptic Cauchy problems and the identification of nonlinear corrosion. https://arxiv.org/abs/math/0411481

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