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

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 frommeasured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated with the wave equation. We prove in dimension n >= 2 that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the absorption coefficient and the electric potential, and we establish Holder-type stability.