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Zap. Nauchn. Sem. POMI, 2009, Volume 369, Pages 164–201 (Mi znsl3526)  

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

Asymptotic modeling of a problem with contrasting stiffness

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: An asymptotic model is found of the Neumann problem for second-order differential equation with piecewise constant coefficients in the composite domain $\Omega\cup\omega$ which are small of order $O(\varepsilon)$ in the subdomain $\omega$. Namely a domain $\Omega(\varepsilon)$ with a singular perturbed boundary is constructed whose solution gives a two-term asymptotic, i.e., of the increased accuracy $O(\varepsilon^2)$, approximation solution for the restriction on $\Omega$ of the original problem. In contrast to other singularly perturbed problems, in the case of contrasting stiffness modeling requires for constructing the contour $\partial\Omega(\varepsilon)$ with ledges, i.e., boundary fragments with curvature $O(\varepsilon^{-1})$. Bibl. – 33 titles.

Key words and phrases: asymptotics, singularly disturbed boundary with ledges, energy functional, modiling.

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English version:
Journal of Mathematical Sciences (New York), 2010, 167:5, 692–712

UDC: 517.956.223+517.956.8
Received: 15.09.2009

Citation: S. A. Nazarov, “Asymptotic modeling of a problem with contrasting stiffness”, Mathematical problems in the theory of wave propagation. Part 38, Zap. Nauchn. Sem. POMI, 369, POMI, St. Petersburg, 2009, 164–201; J. Math. Sci. (N. Y.), 167:5 (2010), 692–712

Citation in format AMSBIB
\Bibitem{Naz09}
\by S.~A.~Nazarov
\paper Asymptotic modeling of a~problem with contrasting stiffness
\inbook Mathematical problems in the theory of wave propagation. Part~38
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 369
\pages 164--201
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3526}
\elib{http://elibrary.ru/item.asp?id=15336400}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 167
\issue 5
\pages 692--712
\crossref{https://doi.org/10.1007/s10958-010-9955-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953914154}


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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. 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
    2. 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
    3. Nazarov S.A., “Perturbation of an eigenvalue in the continuous spectrum of a waveguide with an asymmetric obstacle”, Dokl. Math., 84:2 (2011), 734–739  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Записки научных семинаров ПОМИ
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