3 papers
math.AP2026
The Follow-the-Leader scheme with non-monotone velocity
Marco Di Francesco
This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity ma…
math.AP2024
A system of continuity equations with nonlocal interactions of Morse type
Marco Di Francesco, Valeria Iorio
We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest i…
math.AP2024
Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux
M. Di Francesco, S. Fagioli, E. Radici
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for…