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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 2, Pages 345–362 (Mi izv1244)  

This article is cited in 2 scientific papers (total in 2 papers)

The structure of a neighborhood of a homogeneous cycle in a medium with diffusion

A. Yu. Kolesov


Abstract: On the basis of the Krylov–Bogolyubov–Mitropol'skii asymptotic method a technique is developed for constructing a normal form in a neighborhood of a homogeneous cycle of a boundary value problem of “reaction-diffusion” type which loses stability as some parameters change. Its applications are illustrated with a number of substantial examples. In particular, dynamic effects connected with the generation of a cycle from a densification of trajectories are considered.
Bibliography: 28 titles.

Full text: PDF file (1984 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:2, 355–372

Bibliographic databases:

UDC: 517.926
MSC: Primary 35K57; Secondary 35B35, 34C35, 92A15
Received: 05.06.1987

Citation: A. Yu. Kolesov, “The structure of a neighborhood of a homogeneous cycle in a medium with diffusion”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 345–362; Math. USSR-Izv., 34:2 (1990), 355–372

Citation in format AMSBIB
\Bibitem{Kol89}
\by A.~Yu.~Kolesov
\paper The structure of a~neighborhood of a~homogeneous cycle in a~medium with diffusion
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 2
\pages 345--362
\mathnet{http://mi.mathnet.ru/izv1244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=998300}
\zmath{https://zbmath.org/?q=an:0810.58019|0681.58021}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 2
\pages 355--372
\crossref{https://doi.org/10.1070/IM1990v034n02ABEH000651}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Kolesov, N. Kh. Rozov, “Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation”, Theoret. and Math. Phys., 134:3 (2003), 308–325  mathnet  crossref  crossref  mathscinet  isi
    2. A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “The problem of birth of autowaves in parabolic systems with small diffusion”, Sb. Math., 198:11 (2007), 1599–1636  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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