# WELL-POSEDNESS FOR A MONOTONE SOLVER FOR TRAFFIC JUNCTIONS

Abstract : In this paper we aim at proving well-posedness of solutions obtained as vanishing viscosity limits for the Cauchy problem on a traffic junction where $m$ incoming and $n$ outgoing roads meet. The traffic on each road is governed by a scalar conservation law $\rho_{h,t} + f_h (\rho_h)_x =0, for$h =1,..., m+n\$. Our proof relies upon the complete description of the set of road-wise constant solutions and its properties, which is of some interest on its own. Then we introduce a family of Kruzhkov-type adapted entropies at the junction and state a definition of admissible solution in the same spirit as in [1, 2, 4, 15, 17].

Cited literature [29 references]

https://hal.archives-ouvertes.fr/hal-01312742
Contributor : Boris Andreianov <>
Submitted on : Monday, May 9, 2016 - 6:37:15 AM
Last modification on : Thursday, December 26, 2019 - 12:00:13 PM
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• HAL Id : hal-01312742, version 1
• ARXIV : 1605.01554

### Citation

Boris Andreianov, Guiseppe Maria Coclite, Carlotta Donadello. WELL-POSEDNESS FOR A MONOTONE SOLVER FOR TRAFFIC JUNCTIONS. 2016. ⟨hal-01312742⟩

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