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arXiv · 2608.30859

Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow

Roberta Bianchini·Maya Briani·Benedetto Piccoli
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Abstract

This work provides a traffic flow interpretation of the model recently introduced in \cite{ABS2025}. We adapt the conservation law with discontinuous gradient-dependent flux to a macroscopic traffic setting, assuming concave flux functions $f(u)$ and $g(u)$ defined on the density domain $[0,u_{\max}]$. To prevent violations of the maximal density constraint, we introduce modified Riemann Solvers tailored to this setting and generalize the existence theory for weak solutions developed in \cite{ABS2025}. Finally, we construct Riemann Solvers for a broader two-phase model incorporating a free-flow regime, in which $f(u)=g(u)$ on a subset of $[0,u_{\max}]$, and establish existence of weak solutions in this more general framework.

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Roberta Bianchini, Maya Briani, Benedetto Piccoli. 2026-08-31. Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow. https://arxiv.org/abs/2608.30859

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