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Algebra i Analiz, 2010, Volume 22, Issue 6, Pages 109–126 (Mi aa1216)  
This article is cited in 4 scientific papers (total in 6 papers)

Research Papers

On asymptotic approximations of solutions of an equation with a small parameter

A. M. Il'ina, E. F. Lelikovab

a Chelyabinsk State University, Chelyabinsk, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
Full-text PDF (273 kB) Citations (6)
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Abstract: A second order elliptic equation with a small parameter at one of the highest order derivatives is considered in a three-dimensional domain. The limiting equation is a collection of two-dimensional elliptic equations in two-dimensional domains depending on one parameter. By the method of matching of asymptotic expansions, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter.
Keywords: asymptotic, boundary value problem, small parameter, matching of asymptotic expansions.
Received: 11.06.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 6, Pages 927–939
DOI: https://doi.org/10.1090/S1061-0022-2011-01177-X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. M. Il'in, E. F. Lelikova, “On asymptotic approximations of solutions of an equation with a small parameter”, Algebra i Analiz, 22:6 (2010), 109–126; St. Petersburg Math. J., 22:6 (2011), 927–939
Citation in format AMSBIB
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\paper On asymptotic approximations of solutions of an equation with a~small parameter
\jour Algebra i Analiz
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Linking options:
  • https://www.mathnet.ru/eng/aa1216
  • https://www.mathnet.ru/eng/aa/v22/i6/p109
    • This publication is cited in the following 6 articles:
    1. A. R. Danilin, “Asymptotics of the Solution of a Bisingular Optimal Distributed Control Problem in a Convex Domain with a Small Parameter Multiplying a Highest Derivative”, Comput. Math. and Math. Phys., 64:5 (2024), 941  crossref
    2. A. R. Danilin, “Asymptotics for solutions of problem on optimally distributed control in convex domain with small parameter at one of higher derivatives”, Ufa Math. J., 15:2 (2023), 42–54  mathnet  crossref
    3. E. F. Lelikova, “On the asymptotics of a solution to an equation with a small parameter in a neighborhood of a point of inflexion”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 132–147  mathnet  crossref  mathscinet  isi  elib
    4. 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
    5. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    6. “Arlen Mikhailovich Il'in. On the occasion of his 80th birsday”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 1–4  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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