Asymptotics of the spectrum of inhomogeneous plate with light-weight stiff inclusions(in Ukrainian)

Author Yu. D. Golovaty, V. M. Hut
yu_holovaty@franko.lviv.ua, v.hut@ukr.net
Lviv Ivan Franko National University

Abstract The Dirichlet spectral problem for an elliptic operator of the fourth order with singularly perturbed coefficients is considered. The problem describes the eigenmodes of a plate with finite number of the stiff and light-weight inclusions of an arbitrary shape. The asymptotic behavior of eigenvalues and eigenfunctions is studied. The number-by-number convergence of the eigenvalues and the corresponding eigenspaces is established. The limit eigenvalue problem involves a non-local boundary conditions. Justification of the asymptotic formulas is based on the norm resolvent convergence of a family of unbounded self-adjoint operators.
Keywords spectral Dirichlet problem; biharmonic operator; eigenvalue; eigenfunction; singular perturbation; asymptotics of spectrum; stiff light inclusions
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Pages 79-94
Volume 40
Issue 1
Year 2013
Journal Matematychni Studii
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