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Modelirovanie i Analiz Informatsionnykh Sistem, 2015, Volume 22, Number 1, Pages 5–22 (Mi mais428)  

This article is cited in 10 scientific papers (total in 10 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
References:
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.
Received: 07.12.2014
English version:
Automatic Control and Computer Sciences, 2015, Volume 49, Issue 7, Pages 493–507
DOI: https://doi.org/10.3103/S0146411615070044
Bibliographic databases:
Document Type: Article
UDC: 517.228.4
Language: Russian
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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\issue 7
\pages 493--507
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Linking options:
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  • https://www.mathnet.ru/eng/mais/v22/i1/p5
  • This publication is cited in the following 10 articles:
    1. Qian Yang, Mingkang Ni, “Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution”, Comput. Math. and Math. Phys., 64:5 (2024), 1130  crossref
    2. Qian Yang, Mingkang Ni, “Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation”, Sci. China Math., 65:2 (2022), 291  crossref
    3. Qian Yang, Mingkang Ni, “ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION”, jaac, 12:6 (2022), 2441  crossref
    4. V. F. Butuzov, “Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations”, Comput. Math. Math. Phys., 61:1 (2021), 53–79  mathnet  crossref  crossref  isi  elib
    5. Mingkang Ni, Qian Yang, “Multizonal internal layers in the singularly perturbed equation with a discontinuous right-hand side”, Comput. Math. Math. Phys., 61:6 (2021), 953–963  mathnet  mathnet  crossref  crossref  isi  scopus
    6. V. F. Butuzov, R. E. Simakov, “Asymptotics of the Solution of a Singularly Perturbed System of Equations with a Multizone Internal Layer”, Diff Equat, 57:4 (2021), 415  crossref
    7. V. F. Butuzov, “Asymptotics of a spike type contrast structure in a problem with a multiple root of the degenerate equation”, Differ. Equ., 55:6 (2019), 758–775  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. V. F. Butuzov, “O kontrastnykh strukturakh s mnogozonnym vnutrennim sloem”, Model. i analiz inform. sistem, 24:3 (2017), 288–308  mathnet  crossref  elib
    10. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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