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This article is cited in 9 scientific papers (total in 9 papers)
Non-selfadjoint singular perturbations and spectral properties of the Orr–Sommerfeld boundary-value problem
S. A. Stepin M. V. Lomonosov Moscow State University
Abstract:
A new approach to the analysis of the asymptotic behaviour (and in particular, of the degree of non-orthogonality) of the eigenfunctions and associated functions of non-selfadjoint singularly perturbed operators and boundary-value problems is suggested; the main attention is paid to the case when the spectrum fails to be lower semicontinuous under singular perturbations. As a model case of the transition from a discrete to a continuous spectrum a Sturm–Liouville problem with a small parameter multiplying the second derivative is considered. Spectrum localization is studied and the growth of the degree of non-orthogonality of the system of eigenfunctions and associated functions of the Orr–Sommerfeld problem as the viscosity vanishes is established.
Received: 16.04.1996
Citation:
S. A. Stepin, “Non-selfadjoint singular perturbations and spectral properties of the Orr–Sommerfeld boundary-value problem”, Mat. Sb., 188:1 (1997), 129–146; Sb. Math., 188:1 (1997), 137–156
Linking options:
https://www.mathnet.ru/eng/sm191https://doi.org/10.1070/SM1997v188n01ABEH000191 https://www.mathnet.ru/eng/sm/v188/i1/p129
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Abstract page: | 643 | Russian version PDF: | 260 | English version PDF: | 8 | References: | 70 | First page: | 1 |
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