On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis
Analysis of PDEs
2010-10-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1010.3683,
title = {On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis},
author = {Francois James and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1010.3683},
year = {2010}
}