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Model. Anal. Inform. Sist., 2016, Volume 23, Number 3, Pages 248–258 (Mi mais495)  

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

Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation

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

a Lomonosov Moscow State University, 119991, Moscow, Leninskie Gory, MSU, faculty of physics
b HU Berlin, Institut für Mathematik, Rudower Chaussee, Berlin, Germany
c Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 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 a 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.

Keywords: singularly perturbed reaction-diffusion equation; asymptotic approximation; periodic solution; boundary layers; Lyapunov stability; region of attraction.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04619_а
14-01-91333_ННИО_а
This work was supported by RFBR and RFBR–DFG projects (pr. 15-01-04619, 14-01-91333).


DOI: https://doi.org/10.18255/1818-1015-2016-3-248-258

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English version:
Automatic Control and Computer Sciences, 2017, 51:7, 606–613

Bibliographic databases:

UDC: 519.624.2
Received: 15.05.2016

Citation: V. F. Butuzov, N. N. Nefedov, L. Recke, K. Schneider, “Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation”, Model. Anal. Inform. Sist., 23:3 (2016), 248–258; Automatic Control and Computer Sciences, 51:7 (2017), 606–613

Citation in format AMSBIB
\Bibitem{ButNefRec16}
\by V.~F.~Butuzov, N.~N.~Nefedov, L.~Recke, K.~Schneider
\paper Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 3
\pages 248--258
\mathnet{http://mi.mathnet.ru/mais495}
\crossref{https://doi.org/10.18255/1818-1015-2016-3-248-258}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520847}
\elib{http://elibrary.ru/item.asp?id=26246291}
\transl
\jour Automatic Control and Computer Sciences
\yr 2017
\vol 51
\issue 7
\pages 606--613
\crossref{https://doi.org/10.3103%2FS0146411617070045}


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    This publication is cited in the following articles:
    1. A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988  mathnet  crossref  crossref  isi  elib
    2. A. A. Bykov, K. E. Ermakova, “Exact solutions of the equations of a nonstationary front with equilibrium points of an infinite order of degeneracy”, Mosc. Univ. Phys. Bull., 73:6 (2018), 583–591  crossref  mathscinet  isi  scopus
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