Homogenization problems in random media

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2010-01-01
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Kontogiannis, Dimitrios
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Gary M. Lieberman
Sunder Sethuraman
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Altmetrics
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Mathematics
Abstract

we study homogenization problems of partial differential equations in random domains. We give an overview of the classical techniques that are used to obtain homogenized equations over simple microstructures (for instance, periodic or almost periodic structures) and we show how we can obtain averaging equations over some particular random configurations. As it will be seen, such methods require ergodic theory, percolation, stochastic processes, in addition to the compactness of solutions and the convergence process.

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Fri Jan 01 00:00:00 UTC 2010