On homogenization of a diffusion perturbed by a periodic reflection invariant vector field

Details On homogenization of a diffusion perturbed by a periodic reflection invariant vector field On homogenization of a diffusion perturbed by a periodic reflection invariant vector field

2006-09-25

arxiv.org/abs/math/0609712v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper the author studies the problem of the homogenization of a diffusion perturbed by a periodic reflection invariant vector field. The vector field is assumed to have fixed direction but varying amplitude. The existence of a homogenized limit is proven and formulas for the effective diffusion constant are given. In dimension $d=1$ the effective diffusion constant is always less than the constant for the pure diffusion. In $d>1$ this property no longer holds in general.

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