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Sbornik: Mathematics, 2013, Volume 204, Issue 6, Pages 824–868
DOI: https://doi.org/10.1070/SM2013v204n06ABEH004322 (Mi sm8129) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Invariant tori for a class of nonlinear evolution equations

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
English version PDF (746 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2013v204n06ABEH004322
Abstract: The paper looks at quite a wide class of nonlinear evolution equations in a Banach space, including the typical boundary value problems for the main wave equations in mathematical physics (the telegraph equation, the equation of a vibrating beam, various equations from the elastic stability and so on). For this class of equations a unified approach to the bifurcation of invariant tori of arbitrary finite dimension is put forward. Namely, the problem of the birth of such tori from the zero equilibrium is investigated under the assumption that in the stability problem for this equilibrium the situation arises close to an infinite-dimensional degeneracy.
Bibliography: 28 titles.
Keywords: nonlinear wave equation, invariant torus, bifurcation, stability, boundary value problem.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00384а
12-01-00155а
Received: 09.04.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 6, Pages 47–92
DOI: https://doi.org/10.4213/sm8129
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 35B05, 35B41, 35K22
Language: English
Original paper language: Russian
Citation: A. Yu. Kolesov, N. Kh. Rozov, “Invariant tori for a class of nonlinear evolution equations”, Mat. Sb., 204:6 (2013), 47–92; Sb. Math., 204:6 (2013), 824–868
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2013v204n06ABEH004322
  • https://www.mathnet.ru/eng/sm/v204/i6/p47
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:596
    Russian version PDF:196
    English version PDF:9
    References:60
    First page:41
     
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