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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
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
Citation:
S. A. Nazarov, M. V. Olyushin, “Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system”, Izv. Math., 61:3 (1997), 619–646
Linking options:
https://www.mathnet.ru/eng/im129https://doi.org/10.1070/im1997v061n03ABEH000129 https://www.mathnet.ru/eng/im/v61/i3/p159
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