Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

Reine Gladys Noucheun; Jean Louis Woukeng

doi:10.20944/preprints202308.1067.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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 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.

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

Computer Science and Mathematics, Applied Mathematics

Comment 1

Received: 6 September 2023
Commenter: Jean Louis Woukeng
Commenter's Conflict of Interests: Author

Comment: This new version contains few changes in the Introduction as well as a new result (Theorem 2) that has been added to the work. We have also added a Conclusion.

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Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains

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