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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 12, paper published in the English version journal (Mi zvmmf10872)  
This article is cited in 3 scientific papers (total in 3 papers)

Papers published in the English version of the journal

Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation

V. F. Butuzova, N. N. Nefedova, L. Reckeb, K. R. Schneiderc

a Faculty of Physics, Moscow State University, Moscow, Russia
b HU Berlin, Institut für Mathematik, Berlin-Adlershof, Germany
c Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Citations (3)
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Abstract: For a singularly perturbed parabolic problem with Dirichlet conditions we prove the existence of a solution periodic in time and with boundary layers at both ends of the space interval in the case that the degenerate equation has a double root. We construct the corresponding asymptotic expansion in the small parameter. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. We also investigate the stability of this solution and the corresponding region of attraction.
Key words: singularly perturbed reaction-diffusion equation, double root of the degenerate equation, initial boundary value problem, asymptotic expansion, asymptotically stable periodic solution, region of attraction.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00437_a
15-01-04619_а
Deutsche Forschungsgemeinschaft RE1336/1-1
This work is supported by RFBR, pr. N 16-01-00437, N 15-01-04619, by the DFG grant RE1336/1-1 and by the program of cooperation of the Moscow State University and the Humboldt University of Berlin.
Received: 03.03.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 12, Pages 1989–2001
DOI: https://doi.org/10.1134/S0965542518120072
Bibliographic databases:
Document Type: Article
Language: English
Citation: V. F. Butuzov, N. N. Nefedov, L. Recke, K. R. Schneider, “Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation”, Comput. Math. Math. Phys., 58:12 (2018), 1989–2001
Citation in format AMSBIB
\Bibitem{ButNefRec18}
\by V.~F.~Butuzov, N.~N.~Nefedov, L.~Recke, K.~R.~Schneider
\paper Existence, asymptotics, stability and region of attraction of a periodic boundary layer solution in case of a double root of the degenerate equation
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 12
\pages 1989--2001
\mathnet{http://mi.mathnet.ru/zvmmf10872}
\crossref{https://doi.org/10.1134/S0965542518120072}
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\elib{https://elibrary.ru/item.asp?id=38683556}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062084425}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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