Giuseppe Maria Coclite (Politecnico di Bari)
Date
Friday March 14, 202510:30 am - 11:30 am
Location
Jeffrey Hall, Room 319Math & Stats Department Colloquium
Friday, March 14, 2025
Time: 10:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Giuseppe Maria Coclite (Politecnico di Bari)
Title: Vanishing viscosity versus Rosenau approximation for scalar conservation laws: the fractional case
Abstract: In this talk, we consider approximations of scalar conservation laws by adding nonlocal diffusive operators. In particular, we consider solutions associated with 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.