Alternating method for solving a biharmonic inverse problem in detection of Robin coefficients

Abstract

In this paper, we are interested in an inverse problem of detection of corrosion for a biharmonic equation which consists to determine the Robin coefficients in the inaccessible part of the boundary from the Riquiert-Neumann data on the accessible one. For this end, we consider the factorisation of the biharmonic problem which gives rise to two Cauchy problems for Laplace and Poisson equations. An algorithm based on an alternative iterative method is proposed allowing to complete the missing Cauchy data and then recover the Robin coefficients. We show the feasibility of this approach by numerical reconstructions.