简单网络多车道宏观交通流模型
A multi-lane macroscopic traffic flow model for simple networks
摘要：
我们证明了由[8]启发的平衡律系统的适定性，该平衡律系统从宏观上描述了多车道道路网络上的交通流。受实际应用的启发，我们允许在速度法和车道数的空间不连续性的存在。这可以描述一些现实的情况。解的存在性来自于Goddom逼近序列的紧性结果，而$L^1$ -稳定性则是通过变量加倍技术得到的。一些数值模拟说明了在样本情况下的解决方案的行为。
英文摘要：
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both in the speed law and in the number of lanes. This allows to describe a number of realistic situations. Existence of solutions follows from compactness results on a sequence of Godunov's approximations, while $L^1$-stability is obtained by the doubling of variables technique. Some numerical simulations illustrate the behaviour of solutions in sample cases.
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