Asymptotics of the spectrum of inhomogeneous plate with light-weight stiff inclusions(in Ukrainian)
The Dirichlet spectral problem for an elliptic operator of the fourthorder with singularly perturbed coefficients is considered.The problem describes the eigenmodes of a plate with finite number ofthe stiff and light-weight inclusions of an arbitrary shape.The asymptotic behavior of eigenvalues and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2013-10-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/texts/2013/40_1/79-94.pdf |
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| Summary: | The Dirichlet spectral problem for an elliptic operator of the fourthorder with singularly perturbed coefficients is considered.The problem describes the eigenmodes of a plate with finite number ofthe stiff and light-weight inclusions of an arbitrary shape.The asymptotic behavior of eigenvalues and eigen-func-tions isstudied. The number-by-number convergence of the eigenvalues and thecorresponding eigenspaces is established. The limit eigenvalueproblem involves a non-local boundary conditions.Justification of the asymptotic formulas is based on the norm resolvent convergenceof a family of unbounded self-adjoint operators. |
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| ISSN: | 1027-4634 |