Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910424398561280 |
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| author | Benoudina, Nardjess Boutaf, Fatima Zohra Kechkar, Nasserdine |
| author_facet | Benoudina, Nardjess Boutaf, Fatima Zohra Kechkar, Nasserdine |
| contents | In this study, the finite volume method is implemented for solving the problem of the semilinear equation: $-d δu+ u=u^q (d, q>0) $with a homogeneous Neumann boundary condition. This problem is equivalent to the known stationary Keller-Segel model, which arises in chemotaxis.After discretization, a nonlinear algebraic system is obtained and solved on the platform Matlab. As a result, many single peaked and multi-peaked shapes in 3D and contour plots can be drawn depending on the parameters d and q. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_17145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domains Benoudina, Nardjess Boutaf, Fatima Zohra Kechkar, Nasserdine Mathematical Physics In this study, the finite volume method is implemented for solving the problem of the semilinear equation: $-d δu+ u=u^q (d, q>0) $with a homogeneous Neumann boundary condition. This problem is equivalent to the known stationary Keller-Segel model, which arises in chemotaxis.After discretization, a nonlinear algebraic system is obtained and solved on the platform Matlab. As a result, many single peaked and multi-peaked shapes in 3D and contour plots can be drawn depending on the parameters d and q. |
| title | Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domains |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2404.17145 |