Solving elliptic Cauchy problems and the identification of nonlinear corrosion

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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.
17 pages

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Analysis of PDEs, 35R30; 35R25; 31B20

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http://salesiana.dossiersoluciones.com/handle/123456789/73320

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411481
 http://arxiv.org/abs/math/0411481

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arXiv