## 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.## References

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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
- Received by editor(s): March 23, 2012
- Received by editor(s) in revised form: November 1, 2012
- Published electronically: December 10, 2014
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3314801