Chemotaxis: from kinetic equations to aggregate dynamics

2011/07/05 by François James, James, François, Nicolas Vauchelet +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics

paper · doi:10.48550/arxiv.1107.0786

openalex publication_date 2011/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An adaptation of the notion of duality solutions, introduced for linear equations with discontinuous coefficients, leads to an existence result. Uniqueness is obtained through a precise definition of the nonlinear flux as well as the complete dynamics of aggregates, i.e. combinations of Dirac masses. Finally a particle method is used to build an adapted numerical scheme.

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• Reaction enhancement by flux-limited chemotaxis

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