摘要:  After reviewing the Lighthill-Whitham model of traffic flow,
a cost functional is considered, depending on the departure
time and on the arrival time of each driver. Under natural assumptions, there exists a unique globally optimal solution, minimizing the total cost to all drivers. In a realistic situation, however, the actual traffic is better described by the Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time. A characterization of the Nash solution is provided, establishing its existence and uniqueness. The costs of the optimal and the equilibrium solution can be compared on some specific examples.

报告人简介: Alberto Bressan is an Eberly Chair Professor in Mathematics of Penn State University. His main research fields include hyperbolic systems of conservation laws, impulsive control of Lagrangian systems, and non-cooperative differential games. He is the recipient of several distinguished international mathematics prizes including Bocher Memorial prize. In 2002 he was invited to give a plenary talk at the International Congress of Mathematicians. He is in the editorial boards of a number of prestigious mathematics journals like Arch. Rational Mech. Anal., Siam J. Math. Anal, J. Differ. Eqns.and so on.