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

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