Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 2, pp. 154-172   https://doi.org/10.15407/mag13.02.154     ( to contents , go back )
https://doi.org/10.15407/mag13.02.154

Homogenized Model of Non-Stationary Diffusion in Porous Media with the Drift

M. Goncharenko

B.Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine
E-mail: marusya61@yahoo.co.uk

L. Khilkova

Institute of Chemical Technology of Eastern Ukrainian National University 31 Volodymyrska Str., Rubizhne 93009, Ukraine
E-mail: LarisaHilkova@gmail.com

Received June 1, 2016, revised November 16, 2016

Abstract

We consider an initial boundary-value problem for a parabolic equation describing non-stationary diffusion in porous media with non-linear absorption on the boundary and the transfer of the diffusing substance by fluid. We prove the existence of the unique solution for this problem. We study the asymptotic behavior of a sequence of solutions when the scale of microstructure tends to zero and obtain the homogenized model of the diffusion process.

Mathematics Subject Classification 2000: 35Q74.
Key words: homogenization, non-stationary diffusion, non-linear boundary condition, homogenized model.

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