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Mathematics of the USSR-Sbornik, 1975, Volume 25, Issue 4, Pages 533–548
DOI: https://doi.org/10.1070/SM1975v025n04ABEH002461 (Mi sm3409) 		 
This article is cited in 30 scientific papers (total in 32 papers)

A method of joining asymptotic expansions for the equation $\varepsilon\Delta u-a(x,y)u_y=f(x,y)$ in a rectangle

A. M. Il'in, E. F. Lelikova
English version PDF (910 kB) Citations (32)
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DOI: https://doi.org/10.1070/SM1975v025n04ABEH002461
Abstract: In the closed rectangle ($0\leqslant x\leqslant l_1$, $0\leqslant y\leqslant l_2$) as $\varepsilon\to0$ an asymptotic expansion of the solution of the Dirichlet problem for the equation indicated in the title is constructed and proved. Near the corners $(0,0)$ and $(l_1,0)$ the method of joining two different asymptotic expansions is employed.
Bibliography: 9 titles.
Received: 12.07.1974
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1975, Volume 96(138), Number 4, Pages 568–583
Bibliographic databases:
UDC: 517.9
MSC: Primary 35J25, 35B40; Secondary 41A60
Language: English
Original paper language: Russian
Citation: A. M. Il'in, E. F. Lelikova, “A method of joining asymptotic expansions for the equation $\varepsilon\Delta u-a(x,y)u_y=f(x,y)$ in a rectangle”, Mat. Sb. (N.S.), 96(138):4 (1975), 568–583; Math. USSR-Sb., 25:4 (1975), 533–548
Citation in format AMSBIB
\Bibitem{IliLel75}
\by A.~M.~Il'in, E.~F.~Lelikova
\paper A~method of joining asymptotic expansions for the equation $\varepsilon\Delta u-a(x,y)u_y=f(x,y)$ in a~rectangle
\jour Mat. Sb. (N.S.)
\yr 1975
\vol 96(138)
\issue 4
\pages 568--583
\mathnet{http://mi.mathnet.ru/sm3409}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=382824}
\zmath{https://zbmath.org/?q=an:0313.35004}
\transl
\jour Math. USSR-Sb.
\yr 1975
\vol 25
\issue 4
\pages 533--548
\crossref{https://doi.org/10.1070/SM1975v025n04ABEH002461}
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  • https://doi.org/10.1070/SM1975v025n04ABEH002461
  • https://www.mathnet.ru/eng/sm/v138/i4/p568
    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:581
    Russian version PDF:359
    English version PDF:14
    References:54
    First page:2
     
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