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arXiv · 2404.17145

Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domains

Nardjess Benoudina·Fatima Zohra Boutaf·Nasserdine Kechkar
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Abstract

In this study, the finite volume method is implemented for solving the problem of the semilinear equation: $-d \delta u+ 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.

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Nardjess Benoudina, Fatima Zohra Boutaf, Nasserdine Kechkar. 2024-04-26. Finite volume simulation of a semi-linear Neumann problem (Keller-Segel model) on rectangular domains. https://arxiv.org/abs/2404.17145

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