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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 1, Pages 62–79 (Mi zvmmf195)  

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

Corner boundary layer in nonlinear singularly perturbed elliptic problems

I. V. Denisov

Tula State Pedagogical University, pr. Lenina 125, Tula, 300026, Russia

Abstract: The Dirichlet problem in a rectangle is considered for the elliptic equation $\varepsilon^2\Delta u=F(u,x,y,\varepsilon)$, where $F(u,x,y,\varepsilon)$ is a nonlinear function of $u$. The method of corner boundary functions is applied to the problem. Assuming that the leading term of the corner part of the asymptotics exists, an asymptotic expansion of the solution is constructed and the remainder is estimated.

Key words: nonlinear singularly perturbed elliptic problems, asymptotic solution method, corner boundary layer.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:1, 59–75

Bibliographic databases:

UDC: 519.632
Received: 13.11.2006
Revised: 05.07.2007

Citation: I. V. Denisov, “Corner boundary layer in nonlinear singularly perturbed elliptic problems”, Zh. Vychisl. Mat. Mat. Fiz., 48:1 (2008), 62–79; Comput. Math. Math. Phys., 48:1 (2008), 59–75

Citation in format AMSBIB
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\by I.~V.~Denisov
\paper Corner boundary layer in nonlinear singularly perturbed elliptic problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 1
\pages 62--79
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\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 1
\pages 59--75
\crossref{https://doi.org/10.1007/s11470-008-1005-7}
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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. I. V. Denisov, T. Yu. Denisova, A. V. Rodionov, “Uglovoi pogransloi v nelineinykh singulyarno vozmuschennykh parabolicheskikh uravneniyakh”, Chebyshevskii sb., 13:3 (2012), 28–46  mathnet
    2. V. F. Butuzov, I. V. Denisov, “Uglovoi pogranichnyi sloi v nelineinykh ellipticheskikh zadachakh, soderzhaschikh proizvodnye pervogo poryadka”, Model. i analiz inform. sistem, 21:1 (2014), 7–31  mathnet
    3. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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