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Zbl 1232.35016
Floden, L.; Holmbom, A.; Olsson, M.; Persson, J.
Detection of scales of heterogeneity and parabolic homogenization applying very weak multiscale convergence. (English)
[J] Ann. Funct. Anal. AFA 2, No. 1, 84-99, electronic only (2011). ISSN 2008-8752/e

The authors study homogenization for certain problems. The approach is not classical; they use a convergence that they call ``very weak multiscale convergence'', already introduced in a previous paper by the same authors [Appl. Math. Lett. 23, No. 10, 1170--1173 (2010; Zbl 1198.35023)]. \par The idea is to find (via the very weak multiscale convergence) the scales of heterogeneity of a problem, even if it seems that one has to guess the frequencies of oscillation of the coefficients of the equation under study. \par As an example, they study the homogenization of particular linear parabolic equations in divergence form in which the matrix defining the operator depends on many variables.
[Fabio Paronetto (Padova)]

MSC 2000:: *35B27 Homogenization, etc.
35K10 Second order parabolic equations, general
46B50 Compactness in normed spaces

Keywords: homogenization; parabolic; two-scale convergence; multiscale convergence; very weak multiscale convergence

Citations: Zbl 1198.35023

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