PreprintarXiv licencearXiv
Traveling Waves for Mixed Nonlocal-Local Systems of Conservation Laws on 𝕊1
Abstract
Non trivial traveling waves in genuinely nonlinear conservation laws hardly appear and, in some cases, scalar nonlocal conservation laws inherit this feature. Here, we show that mixed nonlocal-local systems of conservation laws display a far richer scenario. A variety of traveling waves may exist, different components may travel with different speeds and traveling waves can appear as time-asymptotic limits. Technically, these results need a significant extension of Dafermos' "trend to steady state" theory, exploiting properties of Hamiltonian systems solved by generalized characteristics.
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BibTeX
@misc{colombo2026traveling,
title = {{Traveling Waves for Mixed Nonlocal-Local Systems of Conservation Laws on $\mathbbS^1$}},
author = {Rinaldo M. Colombo and Mauro Garavello and Claudia Nocita},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35771},
eprint = {2610.35771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35771},
}
RIS
TY - UNPB
TI - Traveling Waves for Mixed Nonlocal-Local Systems of Conservation Laws on 𝕊^1
AU - Rinaldo M. Colombo
AU - Mauro Garavello
AU - Claudia Nocita
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35771
UR - https://arxiv.org/abs/2610.35771
AB - Non trivial traveling waves in genuinely nonlinear conservation laws hardly appear and, in some cases, scalar nonlocal conservation laws inherit this feature. Here, we show that mixed nonlocal-local systems of conservation laws display a far richer scenario. A variety of traveling waves may exist, different components may travel with different speeds and traveling waves can appear as time-asymptotic limits. Technically, these results need a significant extension of Dafermos' "trend to steady state" theory, exploiting properties of Hamiltonian systems solved by generalized characteristics.
ER -