报告题目：Models of Traffic Flow

报告人：Alberto Bressan，The Pennsylvania State University

报告时间：2026年4月8日（周三）14:00-16:00

报告地点：20-200

报告摘要：A mathematical description of traffic flow can be achieved by particle models, in terms of a large number of ODEs describing the position of each car, or by continuum models, in terms of a PDE for the traffic density.

After a general introduction, the talk will cover some recent models of traffic flow, and the new mathematical problems that they generate. The first part of the talk will focus on a new macroscopic model described by a conservation law with two fluxes, depending on whether the drivers are in “acceleration mode” or in “deceleration mode”.  In an unstable regime, a Cauchy problem can have infinitely many entropy-admissible solutions. By introducing a probability measure on the family of all these solutions, one obtains a new stochastic process, whose properties are yet to be studied. Such a model can account for the random creation of stop-and-go waves along a highway.

Vehicular traffic can also be analyzed from the point of view of decision theory.  Daily traffic patterns arise as the outcome of the decisions of a large number of drivers, who choose their departure time and route to destination in an optimal way: minimizing a cost for early departure together with a cost for late arrival. In this setting, one can consider globally optimal departure distributions, minimizing the sum of all costs to all drivers, and Nash equilibria, where no driver can lower his own cost by choosing a different departure time. In the second part of the talk, the existence, regularity, and dynamic stability of Nash equilibria will be discussed, together with some open problems.

报告人简介：Professor Bressan is the Eberly Chair professor in Penn State University. His primary field of research is mathematical analysis. He has several important contributions in the theory of hyperbolic conservation laws and was invited to give a plenary talk at International Congress of Mathematicians at Beijing, 2002. He won a number of distinguished awards including the Bôcher Memorial Prize in 2008, and Analysis of Partial Differential Equations, 2007. He became a member of the Royal Norwegian Society of Science and Letters in 2011, and a fellow of the American Mathematical Society in 2012.