PreprintCC BY 4.0arXiv
On a 2x2 system of conservation laws with discontinuous flux
Abstract
We study a one-dimensional 2x2 system of conservation laws with discontinuous flux. We prove the global existence of weak solutions for initial data with sufficiently small total variation. We construct explicitly the associated Riemann solver and analyze its main properties. Finally, we introduce a Glimm-type numerical scheme tailored to the exact Riemann solver and use it to reproduce the wave patterns obtained analytically.
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BibTeX
@misc{chiarello2026system,
title = {{On a $2x2$ system of conservation laws with discontinuous flux}},
author = {Felisia Angela Chiarello and Simone Fagioli and Bastien Polizzi and Massimiliano Daniele Rosini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01858},
eprint = {2610.01858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01858},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a 2x2 system of conservation laws with discontinuous flux
AU - Felisia Angela Chiarello
AU - Simone Fagioli
AU - Bastien Polizzi
AU - Massimiliano Daniele Rosini
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01858
UR - https://arxiv.org/abs/2610.01858
AB - We study a one-dimensional 2x2 system of conservation laws with discontinuous flux. We prove the global existence of weak solutions for initial data with sufficiently small total variation. We construct explicitly the associated Riemann solver and analyze its main properties. Finally, we introduce a Glimm-type numerical scheme tailored to the exact Riemann solver and use it to reproduce the wave patterns obtained analytically.
ER -