Homogenization of spectral problems in bounded domains with doubly high contrasts

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Authors
Babych, Natalia O.
Kamotski, Ilia V.
Smyshlyaev, Valery P.
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Abstract
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Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed. Two-scale limit equations are derived and relate to certain non-standard self-adjoint operators. In particular they explicitly display the first two terms in the asymptotic expansion for the eigenvalues, with a surprising bound for the error of order \epsilon^{5/4} proved.
Comment: 23 pages, 2 figures
Keywords
Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, 35B27, 34E
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