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Networks and Heterogeneous Media

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

  • 1.
    Department of Mathematical Sciences, University of Bath, Bath BA2 7AY
  • Received: 01 April 2008

  • Primary: 35B27; Secondary: 34E.

  • 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 ε5/4 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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  • 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 ε5/4 proved.


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