Abstract
We review our previous results on partial differential equation(PDE) models of traffic flow. These models include the first order PDE models, a nonlocal PDE traffic flow 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.
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