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Izvestiya: Mathematics, 1997, Volume 61, Issue 3, Pages 619–646
DOI: https://doi.org/10.1070/im1997v061n03ABEH000129 (Mi im129) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system

S. A. Nazarova, M. V. Olyushinb

a Saint-Petersburg State University
b Admiral Makarov State Maritime Academy
English version PDF (294 kB) Citations (9)
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DOI: https://doi.org/10.1070/im1997v061n03ABEH000129
Abstract: We study the convergence of solutions of boundary value problems for the Lame system under various boundary conditions in the approximation of a smooth contour by polygonal ones. We explain which cases give rise to a paradox similar to that of Sapondzhyan and Babushka. We carry out a formal asymptotic analysis involving a construction of boundary layers near a rapidly oscillating boundary and asymptotic corrections near corner points.The constructed asymptotic behaviour is shown to be valid.
Received: 29.08.1995
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1997, Volume 61, Issue 3, Pages 159–186
DOI: https://doi.org/10.4213/im129
Bibliographic databases:
MSC: 73K10
Language: English
Original paper language: Russian
Citation: S. A. Nazarov, M. V. Olyushin, “Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system”, Izv. RAN. Ser. Mat., 61:3 (1997), 159–186; Izv. Math., 61:3 (1997), 619–646
Citation in format AMSBIB
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\by S.~A.~Nazarov, M.~V.~Olyushin
\paper Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system
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\yr 1997
\vol 61
\issue 3
\pages 159--186
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\jour Izv. Math.
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  • https://doi.org/10.1070/im1997v061n03ABEH000129
  • https://www.mathnet.ru/eng/im/v61/i3/p159
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:532
    Russian version PDF:248
    English version PDF:19
    References:85
    First page:3
     
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