Strong convergence to the homogenized limit of parabolic equations with random coefficients

Conlon, Joseph; Fahim, Arash

doi:10.1090/S0002-9947-2014-06005-4

Strong convergence to the homogenized limit of parabolic equations with random coefficients
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by Joseph G. Conlon and Arash Fahim PDF

Trans. Amer. Math. Soc. 367 (2015), 3041-3093 Request permission

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. It has previously been shown that if the random environment is translational invariant and ergodic, then solutions of the random equation converge under diffusive scaling to solutions of a homogenized parabolic PDE. In this paper point-wise estimates are obtained on the difference between the averaged solution to the random equation and the solution to the homogenized equation for certain random environments which are strongly mixing.

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