We study an inverse problem of determining time-dependent damping coefficient
and potential appearing in the wave equation in a compact Riemannian manifold
of dimension three or higher. More specifically, we are concerned with the case
of conformally transversally anisotropic manifolds, or in other words, compact
Riemannian manifolds with boundary conformally embedded in a product of the
Euclidean line and a transversal manifold. With an additional assumption of the
attenuated geodesic ray transform being injective on the transversal manifold,
we prove that the knowledge of a certain partial Cauchy data set determines
time-dependent damping coefficient and potential uniquely.Comment: arXiv admin note: text overlap with arXiv:1702.07974 by other author