Asymptotic Expansions of Eigenvalues and Eigenfunctions of a Vibrating System With Stiff Light-Weight Inclusions
We study the spectral properties of a boundary-value problem for an elliptic second-order operator with singularly perturbed coefficients. The problem simulates resonance vibrations of an elastic system with finitely many stiff and, at the same time, light-weight inclusions of any shape. The ratio of the stiffness coefficients of the inclusions and the main body has an order of ε−1 as ε → 0, whereas the ratio of their mass densities has an order of εκ, where κ > 0. The complete asymptotic expansions of the eigenvalues and eigenfunctions of this problem are constructed and justified.
KeywordsAsymptotic Expansion English Translation Elliptic Operator Spectral Problem Concentrate Masse
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