RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zap. Nauchn. Sem. POMI: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (787 kB)
References: PDF file   HTML file

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

UDC: 517.956.223+517.956.8

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} 

• http://mi.mathnet.ru/eng/znsl3526
• http://mi.mathnet.ru/eng/znsl/v369/p164

 SHARE:

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 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
2. Nazarov S.A., “Trapped waves in a cranked waveguide with hard walls”, Acoustical Physics, 57:6 (2011), 764–771
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
•  Number of views: This page: 189 Full text: 40 References: 31