On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis

Francois James (1, 2) , Nicolas Vauchelet (3, 4)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 FDP - Fédération de recherche Denis Poisson
3 LJLL - Laboratoire Jacques-Louis Lions
4 BANG - Nonlinear Analysis for Biology and Geophysical flows

The hydrodynamic limit of a one dimensional kinetic model describing chemotaxis is investigated. The limit system is a conservation law coupled to an elliptic problem for which the macroscopic velocity is possibly discontinuous. Therefore, we need to work with measure-valued densities. After recalling a blow-up result in finite time of regular solutions for the hydrodynamic model, we establish a convergence result of the solutions of the kinetic model towards solutions of a problem limit defined thanks to the flux. Numerical simulations illustrate this convergence result.

Mots clés: chemotaxis; hydrodynamic limit; scalar conservation laws; aggregation

Domaines: Equations aux dérivées partielles [math.AP]

Francois James, Nicolas Vauchelet. On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis. Rivista di Matematica della Università di Parma, 2012, 3 (1), pp.91-113. ⟨hal-00527338⟩