We consider the problem of determining quantitative information about corrosion occurring on an inaccesible part of a specimen. The data for the problem consist of prescribed current flux and voltage measurements on an accessible part of the specimen boundary. The problem is modelled by Laplace's equation with an unknown term γ in the boundary conditions. Our goal is recovering γ from the data. We prove uniqueness under certain regularity assumptions and construct a regularized numerical method for obtaining approximate solutions to the problem. The numerical method, which is based on the assumption that the specimen is a thin plate, is tested in numerical experiments using synthetic data.

We consider the problem of detecting corrosion damage on an inaccessible part of a metallic specimen. Electrostatic data are collected on an accessible part of the boundary. The adoption of a simplified model of corrosion appearance reduces our problem to recovering a functional coefficient in a Robin boundary condition for Laplace's equation. We review theoretical results and numerical methods based on the thin-plate approximation and the Galerkin method. Moreover, we introduce a numerical algorithm based on the quasi-reversibility method.

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Nondestructive evaluation of hidden surface damage by means of stationary thermographic methods requires the construction of approximated solutions of a boundary identification problem for an elliptic equation. In this paper, we describe and test a regularized reconstruction algorithm based on the linearization of this class of inverse problems. The problem is reduced to an infinite linear system whose coefficients come from the Fourier discretization of the Robin boundary value problem for Laplace's equation.

We consider a model for detecting corrosion on the (inaccessible) conducting top side of a metallic plate. We suppose that the effects of corrosion attack consist in material loss. The perturbation so induced in the geometry of the plate is described by a positive function θ . We prove that a suitable data set, collected on the bottom side of the plate, identifies θ uniquely.