Recovering the boundary corrosion from electrical potential distribution using partial boundary data (Q524725)

The authors consider the possibility of detecting a boundary corrosion damage in an inaccessible part of a rectangular shaped electrostatic conductor. This is achieved by using one set of Cauchy data that are specified on an accessible part of the given conductor. This method leads to a nonlinear and ill-posed problem. However, uniqueness is proven in a very general framework and conditional stability of Hölder type is established. The latter one is based on some a-priori assumptions on the unknown impedance as well as on the electrical current input that is specified on the accessible part. Additionally, the authors propose a regularizing scheme involving two regularizing parameters. Precisely, they use the truncation of the series expansion of the solution. Further, the convergence analysis on the explicit regularizing solution is given in terms of a practical average norm for the measurement data.