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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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