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Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains
Version 1
: Received: 7 August 2023 / Approved: 14 August 2023 / Online: 15 August 2023 (11:16:24 CEST)
Version 2 : Received: 1 September 2023 / Approved: 5 September 2023 / Online: 6 September 2023 (14:27:47 CEST)
Version 2 : Received: 1 September 2023 / Approved: 5 September 2023 / Online: 6 September 2023 (14:27:47 CEST)
A peer-reviewed article of this Preprint also exists.
Noucheun, R.G.; Woukeng, J.L. Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains. Mathematics 2023, 11, 3796. Noucheun, R.G.; Woukeng, J.L. Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains. Mathematics 2023, 11, 3796.
Abstract
We carry out in a thin heterogeneous porous layer, the multiscale analysis of Smoluchowski's discrete diffusion-coagulation equations describing the evolution density of diffusing particles that are subject to coagulate in pairs. Assuming that the thin heterogeneous layer is made of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.
Keywords
Homogenizatio; Smoluchowski equation; two-scale convergence; thin domains
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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