| Abstract: |
| Given $(M,g)$, a compact Riemannian manifold of dimension $n\ge 3$, we study the inverse problem of determining time-dependent damping coefficient $a$ and potential $q$ appearing in the wave equation $\p_t^2u-\Delta_g u+a(t, x)\p_tu+q(t, x)u=0$ in $Q=(0, T)\times M$ with $T>0$. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, i.e., compact Riemannian manifolds with boundary that are conformally embedded in a product of the Euclidean line and a transversal manifold $M_0$. Under the assumption that the attenuated geodesic ray transform on $M_0$ is injective, we prove that the knowledge of Cauchy data measured on certain subsets of $\p Q$ determines continuous time-dependent damping coefficient $a$ and potential $q$ uniquely. |
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