Kinetic description and asymptotics for bacterial chemotaxis

The starting point of the study is the so-called Othmer-Dunbar-Alt kinetic model describing chemotaxis of cells. This mesoscopic approach allows to take into account the run-and-tumble process observed during chemotactic motion. A diffusive limit of such system leads to macroscopic equation of Keller-Segel type. A hyperbolic approximation can also be done to derive aggregation equations for which blow up of regular solutions is observed. Then these latter equations are studied using duality techniques to get the existence of measures solutions and their numerical simulations.