Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem

We consider The Cauchy problem for the wave equation with an unknown right hand side, that rapidly oscillates in time. This right hand side is reconstructed from the three-term asymptotics of a solution, which are given at one point of the domain. In this case, an approach developed earlier by one of the authors of this article is used to solve the inverse problems with rapidly oscillating data.