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Tr. Mat. Inst. Steklova, 2005, Volume 250, Pages 112–182 (Mi tm35)  

This article is cited in 4 scientific papers (total in 5 papers)

Buffer Phenomenon in Nonlinear Physics

A. Yu. Kolesova, E. F. Mishchenkob, N. Kh. Rozovc

a P. G. Demidov Yaroslavl State University
b Steklov Mathematical Institute, Russian Academy of Sciences
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The buffer phenomenon is a property of a mathematical model of a nonlinear distributed system to have any predetermined finite number of attractors of the same type (stable equilibrium states, cycles, tori, etc.) for an appropriate choice of its parameters. A rigorous mathematical investigation of the buffer phenomenon has become possible due to the application and development of the apparatus of asymptotic analysis. The buffer property is typical for a wide class of mathematical models that describe many nonlinear processes in physics (radio physics, mechanics, optics, and combustion theory) and are represented by boundary value problems for systems of partial differential equations. The relationship between the buffer phenomenon and the onset of turbulence and dynamical chaos is traced.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 250, 102–168

Bibliographic databases:
UDC: 517.926
Received in October 2004

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer Phenomenon in Nonlinear Physics”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 250, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 112–182; Proc. Steklov Inst. Math., 250 (2005), 102–168

Citation in format AMSBIB
\Bibitem{KolMisRoz05}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper Buffer Phenomenon in Nonlinear Physics
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2005
\vol 250
\pages 112--182
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm35}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200912}
\zmath{https://zbmath.org/?q=an:1138.35001}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 102--168


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “Mathematical aspects of the theory of development of turbulence in the sense of Landau”, Russian Math. Surveys, 63:2 (2008), 221–282  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. N. Kh. Rozov, “Fenomen bufernosti v matematicheskikh modelyakh estestvoznaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 3, 58–63  mathnet  elib
    3. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. S. Bobok, S. D. Glyzin, “Avtokolebaniya reshetok nelineinykh elementov v opyte Skotta”, Model. i analiz inform. sistem, 19:5 (2012), 56–68  mathnet
    5. A. Yu. Kolesov, N. Kh. Rozov, “Invariant tori for a class of nonlinear evolution equations”, Sb. Math., 204:6 (2013), 824–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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