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Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 3, Pages 159–186 (Mi izv129)  

This article is cited in 6 scientific papers (total in 6 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

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.

DOI: https://doi.org/10.4213/im129

Full text: PDF file (2347 kB)
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English version:
Izvestiya: Mathematics, 1997, 61:3, 619–646

Bibliographic databases:

MSC: 73K10
Received: 29.08.1995

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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\pages 159--186
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Nazarov, “Asymptotics of solutions and modelling the problems of elasticity theory in domains with rapidly oscillating boundaries”, Izv. Math., 72:3 (2008), 509–564  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Chechkin, GA, “On the Sapondzhyan-Babuska Paradox”, Applicable Analysis, 87:12 (2008), 1443  crossref  mathscinet  zmath  isi
    3. Nazarov, SA, “Scenarios for the quasistatic growth of a slightly curved and kinked crack”, Pmm Journal of Applied Mathematics and Mechanics, 72:3 (2008), 347  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. S. A. Nazarov, “Asymptotics of trapped modes and eigenvalues below the continuous spectrum of a waveguide with a thin shielding obstacle”, St. Petersburg Math. J., 23:3 (2012), 571–601  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Nazarov S.A., “Trapped Waves in a Cranked Waveguide with Hard Walls”, Acoustical Physics, 57:6 (2011), 764–771  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    6. Dione I. Urquiza J.M., “Finite Element Approximations of the Lame System with Penalized Ideal Contact Boundary Conditions”, Appl. Math. Comput., 223 (2013), 115–126  crossref  mathscinet  zmath  isi  scopus  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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