On the Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients. The Principle of the Limiting Amplitude
Artur Mikhailovich Ishkhanyan, Hovik A. Matevossian · Lobachevskii Journal of Mathematics · 2024
This paper considers the Cauchy problem for a second-order hyperbolic equation with periodic coefficients and zero initial data, and the right-hand side of the equation is the function $$f(x)\,\exp\{-i\,\omega\,t\}$$ , $$\omega>0$$ . For this problem, the limiting amplitude principle and the asymptotic behavior as $$t\to\infty$$ are established.