Numerical simulation of a kinetic model for chemotaxis

This paper is devoted to numerical simulations of a kinetic modeldescribing chemotaxis. This kinetic framework has been investigatedsince the 80's when experimental observations have shown that themotion of bacteria is due to the alternance of 'runs and tumbles'.Since parabolic and hyperbolic models do not take into account themicroscopic movement of individual cells, kinetic models have become of agreat interest. Dolak and Schmeiser (2005) have then proposed a kineticmodel describing the motion of bacteria responding to temporal gradientsof chemoattractants along their paths.An existence result for this system is provided and anumerical scheme relying on a semi-Lagrangian method is presentedand analyzed. An implementation of this scheme allows to obtainnumerical simulations of the model and observe blow-up patterns thatdiffer greatly from the case of Keller-Segel type of models.