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IMI/Publicaţii/BASM/Ediţii/BASM n2(108)-n3(109), 2025/

On the Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients

Authors: A. M. Ishkhanyan, H. A. Matevossian
Keywords: asymptotic behavior of solutions, hyperbolic equation, periodic coefficients, Cauchy problem, Hill operator

Abstract

The paper establishes the asymptotic behavior as $t\to\infty$ and the principle of limiting amplitude of solutions to the Cauchy problem for a second-order hyperbolic equation with periodic coefficients for large values of the time parameter $t$, with zero initial data, where the right side of the equation is the function $f(x)\,\exp\{-i\,\omega\,t\},$ $\omega>0$. To obtain an asymptotic expansion as $t\to\infty$, the basic methods of the spectral theory of differential operators are used, as well as the properties of the spectrum of the Hill operator with periodic coefficients.

A. M. Ishkhanyan
Institute for Physical Research,
National Academy of Sciences of the Republic of Armenia,
Ashtarak 0203, Armenia
E-mail:

H. A. Matevossian
Institute for Physical Research,
National Academy of Sciences of the Republic of Armenia,
Ashtarak 0203, Armenia
E-mail: ,

DOI

https://doi.org/10.56415/basm.y2025.i2-3.p21

Fulltext

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