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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 3, Pages 47–65 (Mi faa3242)  

On the convergence of bloch eigenfunctions in homogenization problems

V. V. Zhikova, S. E. Pastukhovab

a Vladimir State University Named after Alexander and Nikolay Stoletovs, Vladimir, Russia
b Moscow Technological University (MIREA), Moscow, Russia

Abstract: 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, convergence of spectra, Bloch principle, Bloch eigenfunction, double porosity model

Funding Agency Grant Number
Russian Science Foundation 14-11-00398
Supported by the Russian Science Foundation (project 14-11-00398).


DOI: https://doi.org/10.4213/faa3242

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English version:
Functional Analysis and Its Applications, 2016, 50:3, 204–218

Bibliographic databases:

UDC: 517.956.8
Received: 31.05.2015

Citation: V. V. Zhikov, S. E. Pastukhova, “On the convergence of bloch eigenfunctions in homogenization problems”, Funktsional. Anal. i Prilozhen., 50:3 (2016), 47–65; Funct. Anal. Appl., 50:3 (2016), 204–218

Citation in format AMSBIB
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