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Sbornik: Mathematics, 2017, Volume 208, Issue 8, Pages 1088–1112
DOI: https://doi.org/10.1070/SM8883 (Mi sm8883) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
English version PDF (587 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM8883
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”).
Received: 14.12.2016 and 03.04.2017
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 8, Pages 4–30
DOI: https://doi.org/10.4213/sm8883
Bibliographic databases:
Document Type: Article
UDC: 517.928
MSC: Primary 34C29; Secondary 46F05
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1068
    Russian version PDF:124
    English version PDF:10
    References:95
    First page:48
     
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