BENDAHMANE, Mostafa; KARAMI, Fahd; ZAGOUR, Mohammed; MESKINE, Driss

doi:10.1016/j.apm.2019.11.036

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BENDAHMANE, Mostafa
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

KARAMI, Fahd
Ecole Supérieure de Technologie d'Essaouira

ZAGOUR, Mohammed
Ecole Supérieure de Technologie d'Essaouira

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Applied Mathematical Modelling. 2019

Elsevier

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2019

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In this paper, we propose a nonlocal cross-diffusion-fluid system describing the dynamic of interacting multi-populations living in a Newtonian fluid. First, we derive our nonlocal cross-diffusion-fluid system from a nonlocal kinetic-fluid model by performing the micro-macro decomposition method. Second, we prove the existence of weak solutions for the proposed system by applying the nonlinear Galerkin method within a priori estimates and compactness arguments. Based on micro-macro decomposition, we propose and we develop an asymptotic preserving numerical scheme. Finally, we deal with the computational results of the proposed system.< Leer menos

Palabras clave en inglés

Nonlocal diffusion

Kinetic-fluid theory

Nonlinear cross-diffusion

Nonlinear Galerkin method

Asymptotic preserving scheme

Pattern-formation

Finite volume method

Finite element method

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Kinetic-fluid derivation and mathematical analysis of nonlocal cross-diffusion-fluid system

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