Localization of Eigenfunctions in a Narrow Kirchhoff Plate

Localization of Eigenfunctions in a Narrow Kirchhoff Plate

The asymptotics of eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in a narrow two-dimensional domain (a thin Kirchhoff plate with rigidly clamped edges) as its width tends to zero is studied. The effect of localization of eigenfunctions is described, which consis...

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Veröffentlicht in:Russian journal of mathematical physics 2021-04, Vol.28 (2), p.156-178
Hauptverfasser: Bakharev, F. L., Matveenko, S. G.
Format: Artikel
Sprache:eng
Schlagworte:
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Dirichlet problem
Eigenvalues
Eigenvectors
Localization
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung:The asymptotics of eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in a narrow two-dimensional domain (a thin Kirchhoff plate with rigidly clamped edges) as its width tends to zero is studied. The effect of localization of eigenfunctions is described, which consists in their exponential decay when removing away from the most wide plate region. DOI 10.1134/S1061920821020035
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920821020035