Identification of Robin coefficients by the means of boundary measurements

Abstract

We consider the problem of determining the Robin coefficient of some specimen material, by performing measurements on some part of the boundary. An identifiability result is proved for Robin coefficients which are continuous functions with some negative lower bound. Both local and monotone global Lipschitz stability results are established. Finally, a cost function turning the inverse problem into an optimization one is proposed for numerical purposes. This function, which may be viewed as an energetic least-squares one, has an easy-to-compute G-derivative, which encourages us to consider implementing the gradient algorithm in forthcoming numerical experiments.