Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains
In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructur...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/17/3796 |
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| author | Reine Gladys Noucheun Jean Louis Woukeng |
| author_facet | Reine Gladys Noucheun Jean Louis Woukeng |
| author_sort | Reine Gladys Noucheun |
| collection | DOAJ |
| description | In a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in the 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. |
| first_indexed | 2024-03-10T23:17:11Z |
| format | Article |
| id | doaj.art-36ea4d760b874e6aae7a194348c04634 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:17:11Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-36ea4d760b874e6aae7a194348c046342023-11-19T08:32:16ZengMDPI AGMathematics2227-73902023-09-011117379610.3390/math11173796Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous DomainsReine Gladys Noucheun0Jean Louis Woukeng1Department of Mathematics and Computer Science, University of Dschang, Dschang P.O. Box 67, CameroonDepartment of Mathematics and Computer Science, University of Dschang, Dschang P.O. Box 67, CameroonIn a thin heterogeneous porous layer, we carry out a multiscale analysis of Smoluchowski’s discrete diffusion–coagulation equations describing the evolution density of diffusing particles that are subject to coagulation in pairs. Assuming that the thin heterogeneous layer is made up of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in the 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.https://www.mdpi.com/2227-7390/11/17/3796homogenizationSmoluchowski equationtwo-scale convergencethin domains |
| spellingShingle | Reine Gladys Noucheun Jean Louis Woukeng Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains Mathematics homogenization Smoluchowski equation two-scale convergence thin domains |
| title | Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains |
| title_full | Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains |
| title_fullStr | Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains |
| title_full_unstemmed | Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains |
| title_short | Homogenization of Smoluchowski Equations in Thin Heterogeneous Porous Domains |
| title_sort | homogenization of smoluchowski equations in thin heterogeneous porous domains |
| topic | homogenization Smoluchowski equation two-scale convergence thin domains |
| url | https://www.mdpi.com/2227-7390/11/17/3796 |
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