The Bottom of the Spectrum in a Double-Contrast Periodic Model

N. O. Babych ()
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N. O. Babych: University of Bath

Chapter 6 in Integral Methods in Science and Engineering, Volume 1, 2010, pp 53-63 from Springer

Abstract: Abstract A periodic spectral problem in a bounded domain with double inhomogeneities in mass density and stiffness coefficients is considered. A previous study [BKS08] has explored the problem by the method of asymptotic expansions with justification of errors showing that all eigenelements of the homogenized problem really approximate some of the perturbed eigenelements. Within this chapter additional results, partly announced in [BKS08], are obtained on the eigenfunction convergence at the bottom of the spectrum. It is shown that the eigenfunctions, which correspond to the eigenvalues at the bottom of the spectrum, could converge either to zero or to the eigenfunctions of the homogenized problem. The result was obtained by the method of two-scale convergence [Al92, Zh00].

Keywords: Periodicity Cell; Homogenize Problem; Periodic Model; Perforated Domain; Double Porosity Model (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-0-8176-4899-2_6

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