Event description
In this talk we consider approximations of scalar conservation laws by adding nonlocal diffusive operators. In particular, we consider solutions associated to fractional Laplacian and fractional Rosenau perturbations and show that, for any $t>0$, the mutual $L^1$ distance of their profiles is negligible as compared to their common distance to the underlying inviscid entropy solution.
We provide explicit examples showing that our rates are optimal in the supercritical and critical cases, in one space dimension and for strictly convex fluxes. For subcritical equations, our rates are not optimal but they remain explicit.
Those results were obtained in collaboration with N. Alibaud, M. Dalery, and C. Donadello.
This conference is funded by the European Research Council (ERC) under the Horizon Europe research and innovation programme (grant agreement No. 101220121 - project: NEW - Nonuniform Ellipticity Widespread).