Abstract
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.
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