Qualitative analysis of some PDE models of traffic flow

We review our previous results on partial differential equation(PDE) models of traffic ow. These models include the first order PDE models, a nonlocal PDE traffic ow model with Arrhenius look-ahead dynamics, and the second order PDE models, a discrete model which captures the essential features of traffic jams and chaotic behavior. We study the well-posedness of such PDE problems, finite time blow-up, front propagation, pattern formation and asymptotic behavior of solutions including the stability of the traveling fronts. Traveling wave solutions are wave front solutions propagating with a constant speed and propagating against traffic. © American Institute of Mathematical Sciences.