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.

Garavello, M., Marcellini, F. (2020). Global weak solutions to the cauchy problem for a two-phase model at a node. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52(2), 1567-1590 [10.1137/19M1265041].

Global weak solutions to the cauchy problem for a two-phase model at a node

Garavello M.;
2020

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.
Articolo in rivista - Articolo scientifico
Cauchy problem; Continuum traffic models; Hyperbolic systems of conservation laws; Networks;
English
2020
52
2
1567
1590
partially_open
Garavello, M., Marcellini, F. (2020). Global weak solutions to the cauchy problem for a two-phase model at a node. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52(2), 1567-1590 [10.1137/19M1265041].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/294228
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