Kinetics models of chemotaxis with temporal sensing mechanism: the parabolic limit and its dynamics
It is well-known that the Keller-Segel type chemotaxis system can be derived as the parabolic limit of the kinetic model describing the velocity-jump process. When the tumbling kernel depends on the temporal gradient of chemical concentration, the rigorous parabolic limit of the kinetic model has not been completely understood. In this talk, we shall report a result for such scenario where the tumbling kernel depending on temporal gradient of chemical concentration is a decreasing smoothed stiff signal response function. We show that parabolic limit of the kinetic model with such tumbling kernel will result in a flux-limited chemotaxis system, which has some distinct features than the classical Keller-Segel model.
