Geodesic
On the convergence of bloch eigenfunctions in homogenization problems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 3, pp. 47-65

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We study the convergence of continuous spectrum eigenfunctions for differential operators of divergence type with $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. Two cases are considered, the case of classical homogenization, where the coefficient matrix satisfies the ellipticity condition uniformly with respect to $\varepsilon$, and the case of two-scale homogenization, where the coefficient matrix has two phases and is highly contrast with hard-to-soft-phase contrast ratio $1\,{:}\,\varepsilon^2$.
Keywords: homogenization, two-scale convergence, Bloch principle, Bloch eigenfunction, double porosity model.
Mots-clés : convergence of spectra 
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     author = {V. V. Zhikov and S. E. Pastukhova},
     title = {On the convergence of bloch eigenfunctions in homogenization problems},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {47--65},
     publisher = {mathdoc},
     volume = {50},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_3_a3/}
}
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V. V. Zhikov; S. E. Pastukhova. On the convergence of bloch eigenfunctions in homogenization problems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 3, pp. 47-65. http://geodesic.mathdoc.fr/item/FAA_2016_50_3_a3/