Homogenization of the stochastic double-porosity model

2025/02/05 by Bonhomme, Elise, Duerinckx, Mitia, Gloria, Antoine · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.02847

Abstract

This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic homogenization under very weak conditions, which cover the case of inclusions that are not uniformly bounded or separated. Second, under stronger assumptions, we provide sharp error estimates for the two-scale expansion. The main difficulty is related to the loss of integrability of the control in the resonant zones.

Cited by

• Anderson localization in high-contrast media with random spherical inclusions

Related

• Quantitative estimates for high-contrast random media
• Stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media
• Rate of convergence of a two-scale expansion for some "weakly" stochastic homogenization problems
• Stochastic homogenization for a diffusion-reaction model
• An introduction to the qualitative and quantitative theory of\n homogenization