Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 38 min ago
PreprintarXiv licencearXiv

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

  • Roberta Bianchini
  • Maya Briani
  • Benedetto Piccoli
Open at sourcePDFDOICite

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,umax]. 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,umax], and establish existence of weak solutions in this more general framework.

Related

  1. On a 2x2 system of conservation laws with discontinuous flux
    Felisia Angela Chiarello, Simone Fagioli, Bastien Polizzi +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  2. A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
    Yuanzhe Wei, Chi-Wang Shu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingComputational physicsarXiv
  3. General Periodic Conservation Laws Motivated by Traffic Modeling
    Rinaldo M. Colombo, Mauro Garavello, Claudia Nocita
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Entropy bounded compact stencil Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws
    Deepak Kumar, Pratima Rai, Arvind Patel
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  5. A merged-cell discontinuous Galerkin method for scalar conservation laws on curved domains
    Yong Liu
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{bianchini2026conservation,
  title = {{Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow}},
  author = {Roberta Bianchini and Maya Briani and Benedetto Piccoli},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30859},
  eprint = {2608.30859},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30859},
}
RIS
TY  - UNPB
TI  - Conservation Laws with Discontinuous Flux: A First Application to Traffic Flow
AU  - Roberta Bianchini
AU  - Maya Briani
AU  - Benedetto Piccoli
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30859
UR  - https://arxiv.org/abs/2608.30859
AB  - 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.
ER  -