Homogenization of spectral problems in bounded domains with doubly high contrasts
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Received:
01 April 2008
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Primary: 35B27; Secondary: 34E.
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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 $\varepsilon^{5/4}$ proved.
Citation: Natalia O. Babych, Ilia V. Kamotski, Valery P. Smyshlyaev. Homogenization of spectral problems in bounded domains with doubly high contrasts[J]. Networks and Heterogeneous Media, 2008, 3(3): 413-436. doi: 10.3934/nhm.2008.3.413
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Abstract
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 $\varepsilon^{5/4}$ proved.
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