Stochastic homogenisation of high-contrast media

Using a suitable stochastic version of the compactness argument of [Zhikov VV. On an extension of the method of two-scale convergence and its applications. Sb Math. 2000;191(7-8):973-1014], we develop a probabilistic framework for the analysis of heterogeneous media with high contrast. We show that...

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Bibliographic Details
Published in:Applicable analysis 2019-01, Vol.98 (1-2), p.91-117
Main Authors: Cherdantsev, Mikhail, Cherednichenko, Kirill, Velčić, Igor
Format: Article
Language:English
Subjects:
Alexander Pankov
Contrast media
Convergence
High contrast
Homogenization
random media
stochastic homogenisation
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Summary:Using a suitable stochastic version of the compactness argument of [Zhikov VV. On an extension of the method of two-scale convergence and its applications. Sb Math. 2000;191(7-8):973-1014], we develop a probabilistic framework for the analysis of heterogeneous media with high contrast. We show that an appropriately defined multiscale limit of the field in the original medium satisfies a system of equations corresponding to the coupled 'macroscopic' and 'microscopic' components of the field, giving rise to an analogue of the 'Zhikov function', which represents the effective dispersion of the medium. We demonstrate that, under some lenient conditions within the new framework, the spectra of the original problems converge to the spectrum of their homogenisation limit.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2018.1495327