Funktsional'nyi Analiz i ego Prilozheniya
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (240 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.956.8

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
\Bibitem{ZhiPas16} \by V.~V.~Zhikov, S.~E.~Pastukhova \paper On the convergence of bloch eigenfunctions in homogenization problems \jour Funktsional. Anal. i Prilozhen. \yr 2016 \vol 50 \issue 3 \pages 47--65 \mathnet{http://mi.mathnet.ru/faa3242} \crossref{https://doi.org/10.4213/faa3242} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3526972} \elib{https://elibrary.ru/item.asp?id=27349834} \transl \jour Funct. Anal. Appl. \yr 2016 \vol 50 \issue 3 \pages 204--218 \crossref{https://doi.org/10.1007/s10688-016-0148-x} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000384420000004} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84988432811}