Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube (Q2788919)
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scientific article; zbMATH DE number 6544414
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube |
scientific article; zbMATH DE number 6544414 |
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Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube (English)
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23 February 2016
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eigenvalue and eigenfunction asymptotics
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convergence theorem
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singular perturbations of a domain
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thin toroidal cavity
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Dirichlet and Neumann problems
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lumped mass
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Spectral asymptotic properties for several boundary value problems are studied. These problems involve the Laplace operator in three-dimensional singularly perturbed domains \(\Omega (\varepsilon) = \Omega \setminus \overline{\Gamma}_{\varepsilon}\) with a thin cavity \(\Gamma_{\varepsilon}\). Mixed boundary value problems with the Neumann conditions on \( \partial \Gamma_{\varepsilon}\) and also spectral problems with lumped masses on \(\Gamma_{\varepsilon}\) are considered.
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