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...

Full description

Saved in:
Bibliographic Details
Main Authors: V. M. Hut, Yu. D. Golovaty
Format: Article
Language:deu
Published: Ivan Franko National University of Lviv 2013-10-01
Series:Математичні Студії
Subjects:
Online Access:http://matstud.org.ua/texts/2013/40_1/79-94.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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.
ISSN:1027-4634