Geodesic
On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 71-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : Couette flow, quasiclassical eigenvalue formulas. 
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     title = {On a {Model} {Problem} for the {Orr{\textendash}Sommerfeld} {Equation} with {Linear} {Profile}},
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A. V. D'yachenko; A. A. Shkalikov. On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 71-75. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a9/

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