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arXiv · 2610.35771

Traveling Waves for Mixed Nonlocal-Local Systems of Conservation Laws on $\mathbb{S}^1$

Rinaldo M. Colombo·Mauro Garavello·Claudia Nocita
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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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Rinaldo M. Colombo, Mauro Garavello, Claudia Nocita. 2026-10-26. Traveling Waves for Mixed Nonlocal-Local Systems of Conservation Laws on $\mathbb{S}^1$. https://arxiv.org/abs/2610.35771

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