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PreprintCC BY 4.0arXiv

The Follow-the-Leader scheme with non-monotone velocity

  • Marco Di Francesco
Open at sourcePDFDOICite

Abstract

This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity map is \emph{non monotone}. The result is based on a discrete maximum principle, on BV estimates of the approximated density, and on the characterization of the limit as entropy solution in the sense of Kru\v zkov.

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Cite

BibTeXRIS
BibTeX
@misc{francesco2026followtheleader,
  title = {{The Follow-the-Leader scheme with non-monotone velocity}},
  author = {Marco Di Francesco},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.28195},
  eprint = {2607.28195},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.28195},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Follow-the-Leader scheme with non-monotone velocity
AU  - Marco Di Francesco
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2607.28195
UR  - https://arxiv.org/abs/2607.28195
AB  - This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity map is \emph{non monotone}. The result is based on a discrete maximum principle, on BV estimates of the approximated density, and on the characterization of the limit as entropy solution in the sense of Kru\v zkov.
ER  -