Non-selfadjoint singular perturbations and spectral properties of the Orr-Sommerfeld boundary-value problemстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация: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.