Recovery of a fast oscillating free term in the wave equation by asymptotics of the solution

Abstract

Three problems about recovery of a high-frequency free term in the one-dimension wave equation with homogeneous initial-boundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that the free term can be completely recovered from a specific data about incomplete (three-terms) asymptotics of the solution. Before formulation of the each problem about recovery of free term, construction and justification of the asymptotics of the solution of original initial-boundary problem are given.