Asymptotic Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients (Case: H0 > 0)

The main goal of this article is to study the behavior of solutions of non-stationary problems at large timescales, namely, to obtain an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coeffic...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2022-08, Vol.10 (16), p.2963
Main Authors: Matevossian, Hovik A., Korovina, Maria V., Vestyak, Vladimir A.
Format: Article
Language:English
Subjects:
Analysis
Asymptotes
asymptotic behavior of solutions
Asymptotic methods
Asymptotic properties
Asymptotic series
Cauchy problem
Cauchy problems
Coefficients
Differential equations
Fourier transforms
Functions, Exponential
Hill operator
International conferences
Operators (mathematics)
periodic coefficients
Periodic functions
second-order hyperbolic equation
Spectral theory
Tests, problems and exercises
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The main goal of this article is to study the behavior of solutions of non-stationary problems at large timescales, namely, to obtain an asymptotic expansion characterizing the behavior of the solution of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients at large values of the time parameter t. To obtain an asymptotic expansion as t→∞, 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 in the case when the operator is positive: H0>0.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10162963