SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1567-1590, January 2020.
This paper considers a system of two conservation laws with a Lipschitz continuous flow and deals with solutions to the Cauchy problems at a node. The system considered is the two-phase traffic model, proposed in [R. M. Colombo, F. Marcellini, and M. Rascle, SIAM J. Appl. Math., 70 (2010), pp. 2652--2666]. We are able to provide global in time existence of solutions at a node with a single incoming road and $m$ outgoing roads. Neither assumptions on the smallness of the total variation of initial data are required, as usual in the case of systems, nor on the range of the initial data.

中文翻译：

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节点两相模型柯西问题的整体弱解

SIAM数学分析杂志，第52卷，第2期，第1567-1590页，2020年1月。
本文考虑具有Lipschitz连续流的两个守恒定律的系统，并处理节点上柯西问题的解决方案。所考虑的系统是两阶段交通模型，在[RM Colombo，F. Marcellini，and M. Rascle，SIAM J. Appl。数学，70（2010），第2652--2666页]。我们能够在具有单个传入道路和$ m $传出道路的节点上提供全局及时的解决方案。不需要像通常在系统中那样假设初始数据的总变化量很小，也不需要假设初始数据的范围。