Behavior as t → ∞ of Solutions of a Mixed Problem for a Hyperbolic Equation with Periodic Coefficients on the Semi-Axis

In this paper, we consider the asymptotic behavior (as t→∞) of solutions as an initial boundary value problem for a second-order hyperbolic equation with periodic coefficients on the semi-axis (x>0). The main approach to studying the problem under consideration is based on the spectral theory of differential operators, as well as on the properties of the spectrum (σ(H0)) of the one-dimensional Schrödinger operator H0 with periodic coefficients p(x) and q(x).