Homogenization of spectral problems in bounded domains with doubly high contrasts

Natalia O. Babych; Ilia V. Kamotski; Valery P. Smyshlyaev

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arXiv · 0711.2405

Homogenization of spectral problems in bounded domains with doubly high contrasts

Natalia O. Babych·Ilia V. Kamotski·Valery P. Smyshlyaev

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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 ε^{5/4} proved.

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Natalia O. Babych, Ilia V. Kamotski, Valery P. Smyshlyaev. 2007-11-15. Homogenization of spectral problems in bounded domains with doubly high contrasts. https://arxiv.org/abs/0711.2405

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