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arXiv · 1305.0837

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

Joseph G. Conlon·Arash Fahim
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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 Poincar\'{e} 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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Joseph G. Conlon, Arash Fahim. 2013-05-03. Strong Convergence to the homogenized limit of parabolic equations with random coefficients II. https://arxiv.org/abs/1305.0837

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