RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 12, paper published in the English version journal (Mi zvmmf10872)  

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

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.


References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:12, 1989–2001

Bibliographic databases:

Received: 03.03.2017
Language:

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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000458237300008}
\elib{http://elibrary.ru/item.asp?id=38683556}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062084425}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10872

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:112
    References:22

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020