## ALTERNATING METHOD FOR SOLVING A BIHARMONIC INVERSE PROBLEM IN DETECTION OF ROBIN COEFFICIENTS

## ALTERNATING METHOD FOR SOLVING A BIHARMONIC INVERSE PROBLEM IN DETECTION OF ROBIN COEFFICIENTS

*B. Jouilik, J. Daoudi, C. Tajani, J. Abouchabaka*

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## Abstract

In this paper, we are interested in an inverse problem of detection of cor- rosion for a biharmonic equation which consists to determin the Robin coe cients 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 coe cients. We show the feasibility of this approach by numerical reconstructions.

## Keywords

ill-posed problem, inverse problem, biharmonic equation, nite element method.