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On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions

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Abstract

We find the asymptotics of the eigenpairs of the Dirichlet and Neumann spectral problems for the Laplace operator in a domain separated by several partitions with holes of small diameters and splitting into several independent cells in the limit as the diameters tend to zero. Using asymptotic methods for singularly perturbed domains, we study the splitting of a multiple eigenvalue of the limit problems, for example, the zero eigenvalue under the Neumann boundary conditions, and the localization of the eigenfunction in the case of a simple eigenvalue.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, 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 by V. Potapchouck

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Nazarov, S.A. On the Eigenvalues and Eigenfunctions of the Dirichlet and Neumann Problems in a Domain with Perforated Partitions. Diff Equat 57, 736–752 (2021). https://doi.org/10.1134/S0012266121060045

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  • DOI: https://doi.org/10.1134/S0012266121060045

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