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Model. Anal. Inform. Sist., 2015, Volume 22, Number 1, Pages 5–22 (Mi mais428)  

This article is cited in 3 scientific papers (total in 3 papers)

Singularly perturbed boundary value problem with multizonal interior transitional layer

V. F. Butuzov

M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia

Abstract: Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal.

Keywords: singularly perturbed equation, interior transitional layer, asymptotic expansion of solution.

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English version:
Automatic Control and Computer Sciences, 2015, 49:7, 493–507

Bibliographic databases:

UDC: 517.228.4
Received: 07.12.2014

Citation: V. F. Butuzov, “Singularly perturbed boundary value problem with multizonal interior transitional layer”, Model. Anal. Inform. Sist., 22:1 (2015), 5–22; Automatic Control and Computer Sciences, 49:7 (2015), 493–507

Citation in format AMSBIB
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\pages 5--22
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\jour Automatic Control and Computer Sciences
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\pages 493--507
\crossref{https://doi.org/10.3103/S0146411615070044}
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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. V. F. Butuzov, A. I. Bychkov, “Nachalno-kraevaya zadacha dlya singulyarno vozmuschennogo parabolicheskogo uravneniya v sluchayakh dvukratnogo i trekhkratnogo kornya vyrozhdennogo uravneniya”, Chebyshevskii sb., 16:4 (2015), 41–76  mathnet  elib
    2. V. F. Butuzov, “O kontrastnykh strukturakh s mnogozonnym vnutrennim sloem”, Model. i analiz inform. sistem, 24:3 (2017), 288–308  mathnet  crossref  elib
    3. V. F. Butuzov, “On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer”, Comput. Math. Math. Phys., 58:6 (2018), 925–949  mathnet  crossref  crossref  isi  elib
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