On the Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients. The Principle of the Limiting Amplitude

被引：0
作者：
Ishkhanyan, A. M. [1 ]
Matevossian, H. A. [2 ]
机构：
[1] Natl Acad Sci, Inst Phys Res, Ashtarak 0204, Armenia
[2] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia
来源：
LOBACHEVSKII JOURNAL OF MATHEMATICS | 2024年 / 45卷 / 08期
关键词：
asymptotic behavior of solutions; hyperbolic equation; periodic coefficients; Cauchy problem; Hill operator; principle of the limiting amplitude;
D O I：
10.1134/S1995080224604326
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 -> infinity are established.
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收藏
页码：3548 / 3558
页数：11
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