Chemotaxis: from kinetic equations to aggregate dynamics
- 275 Downloads
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.
Mathematics Subject Classification (2010)35B40 35D30 35L60 35Q92
KeywordsDuality solutions Non local conservation equations Hydrodynamic limit Measure-valued solutions Chemotaxis
- 17.James, F., Vauchelet, N.: On the hydrodynamical limit for a one dimensional kinetic model of cell aggregation by chemotaxis. Riv. Mat. Univ. Parma. (to appear)Google Scholar
- 24.Perthame, B.: Transport Equations in Biology. Frontiers in Mathematics. Birkäuser, BaselGoogle Scholar