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Two-scale Convergence for Partial Differential Equations with Random Coefficients

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Abstract

We introduce the notion of two-scale convergence for partialdifferential equations with random coefficients that gives a veryefficient way of finding homogenized differential equations withrandom coefficients. For an application, we find the homogenizedmatrices for linear second order elliptic equations with randomcoefficients. We suggest a natural way of finding the two-scalelimit of second order equations by considering the flux term.

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