Stability estimate of a time-dependent matrix potential in a wave equation from partial boundary data

Abstract

We analyze the stability in the inverse problem of determining the zeroth-order time-dependent matrix potential appearing in an initial-boundary value problem associated to a wave equation from the partial boundary observations. A log-log-type stability estimate is obtained for the zeroth-order coefficient using the geometric optics solutions, Carleman estimate, and the light-ray transform. This problem is related to the inverse problem of stable determination of a semilinear term associated with a nonlinear hyperbolic system from the boundary measurements.