Stochastic homogenisation of high-contrast media. Issue 1 (25th January 2019)

• Record Type: Journal Article
• Authors: Cherdantsev, Mikhail; Cherednichenko, Kirill; Velčić, Igor
• Is Part Of: Applicable analysis. Volume 98:Issue 1/2(2019)
• Page Start: 91
• Page End: 117
• Publication Date: 2019-01-25
• Subjects: Alexander Pankov; High contrast -- random media -- stochastic homogenisation; 74Q15 -- 35B40 -- 47A10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1495327
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: 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.