Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Reine Gladys Noucheun; Jean Louis Woukeng

doi:10.20944/preprints202308.1067.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

We carry out in a thin heterogeneous porous layer, the multiscale analysis of a set of Smoluchowski's discrete diffusion-coagulation equations describing the evolution density of diffusion particles that are prone 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. To achieve our goal, we use the concept of two-scale convergence adapted to thin heterogeneous media.

Homogenizatio; Smoluchowski equation; two-scale convergence; thin domains

Computer Science and Mathematics, Applied Mathematics

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Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

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