Newton-Kantorovich method for three-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time-dependent data

A special version of the Newton-Kantorovich method is applied to the three-dimensional potential inverse scattering problem in the time domain. The related hyperbolic Cauchy problem with data on the side of the time cylinder is solved by the quasi-reversibility method, and a new stability theorem is established by Carleman-type estimates. The geometrical convergence of the Newton-Kantorovich method, used here, is also established.