The rate of convergence to the asymptotics for the wave equation in an exterior domain

In this paper we consider the mixed problem for the wave equation exterior to a non-trapping obstacle in odd space dimensions. We derive a rate of the convergence of the solution for the mixed problem to a solution for the Cauchy problem. As a by-product, we are able to find out the radiation field of solutions to the mixed problem in terms of the scattering data.