Strong Convergence to the homogenized limit of parabolic equations with random coefficients II

2013/05/03 by Conlon, Joseph G., Fahim, Arash
#35R60 #60J75 #81T08 #82B20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.0837

Abstract

This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. In [11] rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincaré inequality were obtained. Here these results are extended to certain environments in which correlations can have arbitrarily small power law decay. Similar results for discrete elliptic equations were obtained in [12].

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