Optimal stability for a first order coefficient in a non-self-adjoint wave equation from dirichlet-to-neumann map

Abstract: This paper is focused 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 H{\"o}lder type for the inverse problem under consideration. The proof involves the reduction to an auxiliary inverse problem for an electromagnetic wave equation and the use of an appropriate Carleman estimate.