\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2010, Volume 28, Issue 4: 1311-1343. Doi: 10.3934/dcds.2010.28.1311
This issue Previous Article Measures related to metric complexity Next Article On systems of differential equations with extrinsic oscillation

Homogenization and corrector theory for linear transport in random media

  • 1.

    Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027

  • 2.

    Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027

Received:  September 30, 2009
Revised:  January 31, 2010
Published:  November 2010
Abstract Related Papers Cited by
    Abstract
  • We consider the theory of correctors to homogenization in stationary transport equations with rapidly oscillating, random coefficients. Let ε << 1 be the ratio of the correlation length in the random medium to the overall distance of propagation. As ε $ \downarrow 0$, we show that the heterogeneous transport solution is well-approximated by a homogeneous transport solution. We then show that the rescaled corrector converges in (probability) distribution and weakly in the space and velocity variables, to a Gaussian process as an application of a central limit result. The latter result requires strong assumptions on the statistical structure of randomness and is proved for random processes constructed by means of a Poisson point process.
    Mathematics Subject Classification: Primary: 35B40, 35B27, 35R60; Secondary: 60G55, 60F99.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(85) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences