Stability estimate in the determination of a time-dependent coefficient for hyperbolic equation by partial Dirichlet-to-Neumann map

ABSTRACTIn this paper, we obtain stability estimates of recovery a time dependent coefficient in a wave equation, from partial observations on . We show in dimension n greater than two a log-type stability estimate in the determination of q from the local Dirichlet-to-Neumann map. Additionally, we prove that it can be stably recovered in a larger region of the domain by enlarging the set of data.