M611

We study the homogenisation problem for elliptic operators with high-contrast random coefficients describing a two-phase composite with the heterogeneity scale $\epsilon$ made up of small inclusions randomly distributed in a matrix component. It is assumed that the coefficients of the operator are of order one in the matrix component and of order $\epsilon^2$ in the inclusions (so-called double porosity scaling). High-contrast composites receive special attention in scientific community due to the band-gap structure of their spectrum. In this talk I will give an introduction to the high-contrast setting followed by an overview of our recent results in the topic and some ongoing work.

Mikhail Cherdantsev