This article is cited in 1 paper

Homogenized model of non-stationary diffusion in porous media with the drift

M. Goncharenko^a, L. Khilkova<sup>b

a</sup> B.Verkin Institute for Low Temperature Physics and Engineering, of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv 61103, Ukraine
^b Institute of Chemical Technology of Eastern Ukrainian National University, 31 Volodymyrska Str., Rubizhne 93009, Ukraine

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.

Key words and phrases: homogenization, non-stationary diffusion, non-linear boundary condition, homogenized model.

MSC: 35Q74

Received: 01.06.2016
Revised: 16.11.2016

Language: English

DOI: 10.15407/mag13.02.154

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