Simultaneous determination of two coefficients in the Riemannian hyperbolic equation from boundary measurements

Abstract: In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n \geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uni