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Mat. Sb., 2017, Volume 208, Number 8, Pages 4–30 (Mi msb8883)  

Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations

V. S. Belonosovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: This paper is concerned with parametric resonance under nonlinear periodic perturbations of differential equations which are abstract analogues of hyperbolic systems. A modification of the Krylov-Bogolyubov averaging method capable of circumventing the well-known small divisor problem is applied to reduce the description of solutions of perturbed equations at resonance to the study of autonomous dynamical systems in finite-dimensional spaces.
Bibliography: 28 titles.

Keywords: hyperbolic equations, parametric resonance, averaging method.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations I.5П
This work was supported by the Presidium of the Russian Academy of Sciences (fundamental research programme I5.П “Problems of creation of high-performance, distributed and cloud systems and technologies. Intellectual and informative technologies and systems”).


DOI: https://doi.org/10.4213/sm8883

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English version:
Sbornik: Mathematics, 2017, 208:8, 1088–1112

Bibliographic databases:

UDC: 517.928
MSC: Primary 34C29; Secondary 46F05
Received: 14.12.2016 and 03.04.2017

Citation: V. S. Belonosov, “Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations”, Mat. Sb., 208:8 (2017), 4–30; Sb. Math., 208:8 (2017), 1088–1112

Citation in format AMSBIB
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