Hyperbolic Equation with Rapidly Oscillating Data: Reconstruction of the Small Lowest Order Coefficient and the Right-Hand Side from Partial Asymptotics of the Solution

Abstract We consider the Cauchy problem for a one-dimensional hyperbolic equation. The lowest order coefficient and the right-hand side oscillate in time at a high frequency, and the amplitude of the lowest order coefficient is small. The way of reconstructing these oscillating functions from partial solution asymptotics given at a certain point of the domain is studied.