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

S. A. Nazarov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 31-48.

Résumé

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.

Détail

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

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