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Modeling of a singularly perturbed spectral problem by means of self-adjoint extensions of the operators of the limit problems

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Abstract

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.

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Authors and Affiliations

  1. St. Petersburg State University, St.-Petersburg, Russia

    S. A. Nazarov

  2. Institute of Problems of Mechanical Engineering, St.-Petersburg, Russia

    S. A. Nazarov

  3. Saint-Petersburg State Polytechnical University, St-Petersburg, Russia

    S. A. Nazarov

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  1. S. A. Nazarov
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Correspondence to S. A. Nazarov.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 49, No. 1, pp. 31–48, 2015

Original Russian Text Copyright © by S. A. Nazarov

Supported by RFBR grant 15-01-02175.

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Nazarov, S.A. Modeling of a singularly perturbed spectral problem by means of self-adjoint extensions of the operators of the limit problems. Funct Anal Its Appl 49, 25–39 (2015). https://doi.org/10.1007/s10688-015-0080-5

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  • DOI: https://doi.org/10.1007/s10688-015-0080-5

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