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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1990, Volume 30, Number 2, Pages 254–269 (Mi zvmmf3308)  

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

Asymptotic behaviour of rapidly oscillating contrasting spatial structures

S. A. Kashchenko

Yaroslavl'
References:
Abstract: The asymptotic behaviour of equilibria that rapidly oscillate in the spatial coordinate in a system of two nonlinear parabolic equations with a sufficiently small diffusion coefficient in one of them is investigated. The normalization method is applied to show that the local dynamics of the original system with a small parameter multiplying one of the high-order derivatives is determined by the non-local behaviour of the solutions of a family of special boundary-value problems that are independent of the small parameter.
Received: 22.12.1988
English version:
USSR Computational Mathematics and Mathematical Physics, 1990, Volume 30, Issue 1, Pages 186–197
DOI: https://doi.org/10.1016/0041-5553(90)90028-Q
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: Primary 35B25; Secondary 35B30, 35K57
Language: Russian
Citation: S. A. Kashchenko, “Asymptotic behaviour of rapidly oscillating contrasting spatial structures”, Zh. Vychisl. Mat. Mat. Fiz., 30:2 (1990), 254–269; U.S.S.R. Comput. Math. Math. Phys., 30:1 (1990), 186–197
Citation in format AMSBIB
\Bibitem{Kas90}
\by S.~A.~Kashchenko
\paper Asymptotic behaviour of rapidly oscillating contrasting spatial structures
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1990
\vol 30
\issue 2
\pages 254--269
\mathnet{http://mi.mathnet.ru/zvmmf3308}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1045423}
\zmath{https://zbmath.org/?q=an:0709.35005}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1990
\vol 30
\issue 1
\pages 186--197
\crossref{https://doi.org/10.1016/0041-5553(90)90028-Q}
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  • https://www.mathnet.ru/eng/zvmmf3308
  • https://www.mathnet.ru/eng/zvmmf/v30/i2/p254
  • This publication is cited in the following 4 articles:
    1. I Kashchenko, “The behavior of solutions of an equation with a large spatially distributed control”, J. Phys.: Conf. Ser., 937 (2017), 012021  crossref
    2. D. V. Glazkov, “Lokalnaya dinamika uravneniya vtorogo poryadka s bolshim eksponentsialno raspredelennym zapazdyvaniem i suschestvennym treniem”, Model. i analiz inform. sistem, 22:1 (2015), 65–73  mathnet  mathscinet  elib
    3. Kashchenko S.A., “Dynamics of a Spatially Distributed Logistic Equation with Small Diffusion and Small Delay”, Differ. Equ., 49:12 (2013), 1502–1510  crossref  mathscinet  zmath  isi
    4. S. A. Kashchenko, “Asymptotic form of spatially non-uniform structures in coherent nonlinear optical systems”, U.S.S.R. Comput. Math. Math. Phys., 31:3 (1991), 97–102  mathnet  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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