Stability for a first order coefficient in a non self adjoint wave equation from Dirichlet to Neumann map (Analysis of inverse problems through partial differential equations and related topics)

Abstract

In this presentation we focus on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary data. We show in dimension n greater than two, a stability estimate of Hölder type for the inverse problem under consideration. The proof involves the reduction to an auxiliary inverse problem for an electro-magnetic wave equation and the use of an appropriate Carleman estimate.