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2008, Volume 3, Issue 3: 413-436. Doi: 10.3934/nhm.2008.3.413
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Homogenization of spectral problems in bounded domains with doubly high contrasts

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    Department of Mathematical Sciences, University of Bath, Bath BA2 7AY

Received:  March 31, 2008
Published:  August 2008
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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.
    Mathematics Subject Classification: Primary: 35B27; Secondary: 34E.

    Citation:
    shu

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