道路网上的交通流
Traffic Flow on a Road Network
摘要：
本文研究了一个交通流的流体动力学模型。更确切地说，我们考虑一个单一的守恒律，推导出的汽车数量的守恒，定义在一个道路网络，是一个集合的道路与路口。演化问题是欠定的路口，因此我们选择有一些固定的规则的交通分配加上一个优化标准的流量。我们证明了柯西问题解的存在性、唯一性和稳定性。我们的方法基于波前跟踪方法（B），并且也适用于交叉口（因此包括红绿灯）交通分布的边界数据和不定常系数。
英文摘要：
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, (B), and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.
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