Solving elliptic Cauchy problems and the identification of nonlinear corrosion

2004/11/22 by Giovanni Alessandrini, Alessandrini, Giovanni, Eva Sincich +1
Mathematics · #31B20 #35R25 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:31B20 #msc:35R25 #msc:35R30

paper · pdf · doi:10.48550/arxiv.math/0411481

17 pages

arxiv created 2004/11/22 · arxiv updated 2009/12/01

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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