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


Authors: Joseph G. Conlon and Arash Fahim
Journal: Trans. Amer. Math. Soc. 367 (2015), 3041-3093
MSC (2010): Primary 81T08, 82B20, 35R60, 60J75
DOI: https://doi.org/10.1090/S0002-9947-2014-06005-4
Published electronically: December 10, 2014
MathSciNet review: 3314801
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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. 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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Additional Information

Joseph G. Conlon
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Email: conlon@umich.edu

Arash Fahim
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Address at time of publication: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: fahimara@umich.edu, fahim@math.fsu.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06005-4
Keywords: Euclidean field theory, PDE with random coefficients, homogenization
Received by editor(s): March 23, 2012
Received by editor(s) in revised form: November 1, 2012
Published electronically: December 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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