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- Title
Vibrating Systems with Rigid Light-Weight Inclusions: Asymptotics of the Spectrum and Eigenspaces.
- Authors
Holovatyi, Yu.; Hut, V.
- Abstract
We study the asymptotic behavior of eigenvalues and eigenfunctions of a singularly perturbed boundaryvalue problem for a second-order elliptic operator. The problem simulates natural vibrations of an elastic system with finitely many light-weight inclusions of any shape. The leading terms of the asymptotic representations of eigenelements are constructed with regard for their multiplicities. The justification of the asymptotic formulas is based on the uniform resolvent convergence of a certain family of unbounded self-adjoint operators.
- Subjects
ASYMPTOTIC efficiencies; SPECTRUM analysis; EIGENVALUES; EIGENFUNCTIONS; BOUNDARY value problems; ELLIPTIC operators; ELASTICITY; MULTIPLICITY (Mathematics)
- Publication
Ukrainian Mathematical Journal, 2013, Vol 64, Issue 10, p1495
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-013-0731-8