Electron. J. Diff. Eqns., Vol. 2008(2008), No. 83, pp. 1-36.

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

Joseph G. Conlon

Abstract:
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.

Submitted March 26, 2007. Published May 30, 2008.
Math Subject Classifications: 35R60, 60H30, 60J60.
Key Words: PDE with periodic coefficients; homogenization.

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Joseph G. Conlon
Department of Mathematics, University of Michigan
Ann Arbor, MI 48109-1109, USA
email: conlon@umich.edu

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