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

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.