A HOLDER STABILITY ESTIMATE FOR A COEFFICIENT ̈ INVERSE PROBLEM FOR THE WAVE EQUATION WITH A POINT SOURCE

Abstract

We consider a 3D coefficient inverse problem for the wave-like equation with backscattering non-overdetermined data. The forward problem is the Cauchy problem with the initial condition as the delta-function concentrated at a single location of the point source. We reduce the original problem to a problem with finite differences with respect to two out of three spatial variables and study an inverse problem for it. A stability estimate is stated for this reduced inverse problem.