Coarse-graining and quantitative stochastic homogenization of parabolic equations in high contrast

Abstract

We prove quantitative homogenization results for high contrast parabolic equations with random coefficients depending on both space and time. In particular, we prove that under a sufficient decorrelation assumption the homogenization length scale is bounded by $\exp(C\log^2(1+\Lambda/\lambda)) + C\sqrt{\lambda}$. The proof is based on a parabolic coarse-graining framework which generalizes the results of Armstrong and Kuusi in the elliptic setting.