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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 31–48 (Mi faa3171)  

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

Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit Problems

S. A. Nazarovabc

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
b Saint-Petersburg State Polytechnical University
c St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We use self-adjoint extensions of differential and integral operators to construct an asymptotic model of the Steklov spectral problem describing surface waves over a bank. Estimates of the modeling error are established, and the following unexpected fact is revealed: an appropriate self-adjoint extension of the operators of the limit problems provides an approximation to the eigenvalues not only in the low- and midfrequency ranges of the spectrum but also on part of the high-frequency range.

Keywords: self-adjoint extension, asymptotics of the spectrum, Steklov spectral problem, surface waves

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02175


DOI: https://doi.org/10.4213/faa3171

Full text: PDF file (258 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:1, 25–39

Bibliographic databases:

UDC: 517.984.46+517.958+531.33
Received: 07.12.2012

Citation: S. A. Nazarov, “Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit Problems”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 31–48; Funct. Anal. Appl., 49:1 (2015), 25–39

Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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\pages 31--48
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\pages 25--39
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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. R. Bunoiu, G. Cardone, S. A. Nazarov, “Scalar problems in junctions of rods and a plate II. Self-adjoint extensions and simulation models”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 52:2 (2018), 481–508  crossref  isi
    2. S. A. Nazarov, “The asymptotics of natural oscillations of a long two-dimensional Kirchhoff plate with variable cross-section”, Sb. Math., 209:9 (2018), 1287–1336  mathnet  crossref  crossref  adsnasa  isi  elib
    3. S. A. Nazarov, “Breakdown of cycles and the possibility of opening spectral gaps in a square lattice of thin acoustic waveguides”, Izv. Math., 82:6 (2018), 1148–1195  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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