Chemotaxis: from kinetic equations to aggregate dynamics
Analysis of PDEs
2011-12-05 v2
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.
Cite
@article{arxiv.1107.0786,
title = {Chemotaxis: from kinetic equations to aggregate dynamics},
author = {François James and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1107.0786},
year = {2011}
}
Comments
26 pages