Stable recovery of time dependent coefficient from arbitrary measurements for wave equation

This paper concerns the stability in the inverse problem of determining the time dependent coefficient in the wave equation, from partial knowledge of the Dirichlet-to-Neumann map at the boundary of a bounded domain of interest. We first establish a stability estimate in the determination of the time-dependent coefficient from partial boundary observations. Then we prove that by enlarging the set of data, the unknown coefficient can be stably determined in larger regions. (C) 2019 Elsevier Inc. All rights reserved.