Ibtissem Ben aicha

In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension n≥ 2, stability estimates with respect to the Dirichlet-to-Neumann map of these coefficients provided that are known outside a cloaking regions. Moreover, we prove that it can be stably recovered in larger subsets of the domain by enlarging the set of data

This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in dimension n greater than 2, an H\"older type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schr\"odinger equation and the use of a Carleman estimate designed for elliptic operators.

Cette these est consacree a l’etude de problemes inverses associes a des equations aux derivees partielles hyperboliques et de type Schrodinger.La premiere partie de la these est consacree a l’etude de problemes inverses pour l’equation des ondes. Il s’agit d’examiner les proprietes de stabilite et d’unicite dans l’identification de certains coefficients apparaissant dans l’equation des ondes, a partir de differents types d’observation.La deuxieme partie de cette these, traite du probleme de l’identification du champ magnetique et du potentiel electrique apparaissant dans l’equation du Schrodinger. Nous prouvons que ces coefficients peuvent etre determines de facon stable dans tout le domaine, a partir de donnees de type Neumann. La derivation de ces resultats est basee sur la construction d’un ensemble de solutions de type optique geometrique, adaptees au systeme etudie. Il existe une methode alternative pour l’analyse de ce type de problemes inverses, celle de Bukhgeim-Klibanov, q...