TWO-SCALE CONVERGENCE FOR PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM COEFFICIENTS Pak, Hee-Chul;
We introduce the notion of two-scale convergence for partial differential equations with random coefficients that gives a very efficient way of finding homogenized differential equations with random coefficients. For an application, we find the homogenized matrices for linear second order elliptic equations with random coefficients. We suggest a natural way of finding the two-scale limit of second order equations by considering the flux term.
homogenization;2-scale convergence;partial differential equations with random coefficients;homogenized matrices;second order elliptic differential equations;
SIAM J. Math. Anal., 1992.
Asymptotic Analysis for Periodic Structures, 1978.
Homogenization and Porous Media, 1996.
Applicable Analysis, 2001.
Mathematical Surveys and Monographs, 1997.
Homogenization of Differential Operators and Integral Functionals, 1991.