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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 2, Pages 170–178 (Mi timm817)  
This article is cited in 2 scientific papers (total in 2 papers)

On the asymptotics of a solution to an equation with a small parameter at some of the highest derivatives

E. F. Lelikovaab

a Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (164 kB) Citations (2)
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Abstract: We study the asymptotic behavior of a solution of the first boundary value problem for a second-order elliptic equation in a nonconvex domain with smooth boundary in the case where the small parameter is a factor at only some of the highest derivatives and the limit equation is an ordinary differential equation. Although the limit equation has the same order as the initial equation, the problem under consideration is singulary perturbed. The asymptotic behavior of a solution of this problem is studied by the method of matched asymptotic expansions
Keywords: small parameter, asymptotic expansions.
Received: 17.10.2011
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 281, Issue 1, Pages 95–104
DOI: https://doi.org/10.1134/S008154381305009X
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: E. F. Lelikova, “On the asymptotics of a solution to an equation with a small parameter at some of the highest derivatives”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 170–178; Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 95–104
Citation in format AMSBIB
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\paper On the asymptotics of a~solution to an equation with a~small parameter at some of the highest derivatives
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 170--178
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\vol 281
\issue , suppl. 1
\pages 95--104
\crossref{https://doi.org/10.1134/S008154381305009X}
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  • https://www.mathnet.ru/eng/timm817
  • https://www.mathnet.ru/eng/timm/v18/i2/p170
    • This publication is cited in the following 2 articles:
    1. D. A. Tursunov, U. Z. Erkebaev, “Asimptoticheskoe razlozhenie resheniya zadachi Dirikhle dlya koltsa s osobennostyu na granitse”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 1(39), 42–52  mathnet  crossref  elib
    2. D. A. Tursunov, U. Z. Erkebaev, “Asimptotika resheniya bisingulyarno vozmuschennoi zadachi Dirikhle v koltse s kvadratichnym rostom na granitse”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:2 (2016), 52–61  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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