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Parabolic H-convergence and small-amplitude homogenization

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H-convergence and small-amplitude homogenization is studied for linear parabolic problems with coefficients, which may depend on time. The small-amplitude homogenization consists of taking a sequence of coefficients, whose difference is proportional to a small parameter, and then computing the first correction in the limit. We recall the definition and main results on H-convergence for non-stationary diffusion equation, and prove that the smoothness (with respect to a parameter) is preserved in the process of taking the H-limit, which is essential for our purposes. The explicit expression for the correction is obtained by using a recently introduced parabolic variant of H-mesures.

Keywords: H-measures; homogenization; parabolic equation

Document Type: Research Article


Affiliations: Department of Mathematics, University of Zagreb, Zagreb, Croatia

Publication date: October 1, 2009

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