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arXiv · 2312.16092

Mathematical analysis and multiscale derivation of a nonlinear predator-prey cross-diffusion--fluid system with two chemicals

Mostafa Bendahmane·Fahd Karami·Driss Meskine·Jacques Tagoudjeu·Mohamed Zagour
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Abstract

A nonlinear cross-diffusion--fluid system with chemical terms describing the dynamics of predator-prey living in a Newtonian fluid is proposed in this paper. The existence of a weak solution for the proposed macro-scale system is proved based on the Schauder fixed-point theory, a priori estimates, and compactness arguments. The proposed system is derived from the underlying description delivered by a kinetic-fluid theory model by a multiscale approach. Finally, we discuss the computational results for the proposed macro-scale system in two-dimensional space.

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Mostafa Bendahmane, Fahd Karami, Driss Meskine, Jacques Tagoudjeu, Mohamed Zagour. 2023-12-26. Mathematical analysis and multiscale derivation of a nonlinear predator-prey cross-diffusion--fluid system with two chemicals. https://arxiv.org/abs/2312.16092

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