We consider the problem of determining the corroded portion of the boundary of a n-dimensional body (n=2, 3) and the impedance by two measures on the accessible portion of the boundary. On the unknown boundary part it is assumed the Robin homogeneous condition.

We consider the stability issue for the inverse problem of determining an unknown portion Σ of a two-dimensional simply connected domain from overdetermined boundary data for the Laplace equation. In this paper, we study the case in which Σ is a polygonal line. We prove a Lipschitz stability estimate under further a priori geometric assumptions on Σ.

We consider the problem of determining an unaccessible part of the boundary of a conductor by means of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove logarithmic stability estimate.

We consider an initial-boundary value problem for the classical linear wave equation, where mixed boundary conditions of Dirichlet and Neumann/Robin type are enforced at the endpoints of a bounded interval. First, by a careful application of the method of characteristics, we derive a closed-form representation of the solution for an impulsive Dirichlet data at the left endpoint, and valid for either a Neumann or a Robin data at the right endpoint. Then we devise a reconstruction procedure for identifying both the interval length and the Robin parameter. We provide a corresponding stability result and verify numerically its performance moving from a finite element discretization.

We consider the problem of quantitative non-destructive evaluation of corrosion in a 2D domain representing a thin metallic plate. Corrosion damage is assumed to occur in an inaccessible part of the domain. Reconstruction of the damaged profile is possible by measuring an electrostatic current properly induced by a potential in an accessible part of the boundary (electrical impedance tomography). We present here numerical methods and results based on a formulation of the problem introduced and analyzed in Bacchelli–Vessella, Inverse Problems 22 (2006), where the corroded profile is represented by a polygonal boundary. We resort in particular to the Landweber method and the Brakhage semi-iterative scheme. Numerical results show the reliability of this approach in general situations, including nongraph corroded boundaries.