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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 71–75
DOI: https://doi.org/10.4213/faa208 (Mi faa208) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Brief communications

On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile

A. V. D'yachenkoa, A. A. Shkalikovb

a M. V. Lomonosov Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (139 kB) Citations (15)
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DOI: https://doi.org/10.4213/faa208
Abstract: A model spectral problem of the form $-i\varepsilon y''+xy=\lambda y$ on the finite interval $[-1,1]$ with the Dirichlet boundary conditions is considered. Here $\lambda$ is the spectral parameter and $\varepsilon$ is positive. The behavior of the spectrum of this problem as $\varepsilon\to 0$ is completely investigated. The limit curves are found to which the eigenvalues concentrate and the counting eigenvalue functions along these curves are obtained.
Keywords: the Airy function, Couette flow, quasiclassical eigenvalue formulas.
Received: 29.10.2001
English version:
Functional Analysis and Its Applications, 2002, Volume 36, Issue 3, Pages 228–232
DOI: https://doi.org/10.1023/A:1020158323673
Bibliographic databases:
Document Type: Article
UDC: 517.927+517.928
Language: Russian
Citation: A. V. D'yachenko, A. A. Shkalikov, “On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 71–75; Funct. Anal. Appl., 36:3 (2002), 228–232
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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