Rocky Mountain Journal of Mathematics

Expository Paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions

Alen Alexanderian

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Abstract

We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we provide a gentle introduction to the mathematical theory of homogenization of random media. We also present numerical examples to elucidate the theoretical concepts and results.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 3 (2015), 703-735.

Dates
First available in Project Euclid: 21 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1440168291

Digital Object Identifier
doi:10.1216/RMJ-2015-45-3-703

Mathematical Reviews number (MathSciNet)
MR3385965

Zentralblatt MATH identifier
1354.37085

Subjects
Primary: 37A05: Measure-preserving transformations 37A25: Ergodicity, mixing, rates of mixing 78A48: Composite media; random media 78M40: Homogenization

Keywords
Homogenization random media ergodic dynamical system stationary random field diffusion in random media

Citation

Alexanderian, Alen. Expository Paper: A primer on homogenization of elliptic PDEs with stationary and ergodic random coefficient functions. Rocky Mountain J. Math. 45 (2015), no. 3, 703--735. doi:10.1216/RMJ-2015-45-3-703. https://projecteuclid.org/euclid.rmjm/1440168291


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