Homogenization of spectral problems in bounded domains with doubly high contrasts

2007/11/15 by Babych, Natalia O., Kamotski, Ilia V., Smyshlyaev, Valery P.
#34E #35B27 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0711.2405

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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