entropy solutions 1follow-the-leader scheme 1non-monotone velocity 1particle methods 1scalar conservation laws 1
From the 1 of 3 linked papers with an AI index.
3 papers
math.AP2026
The Follow-the-Leader scheme with non-monotone velocity
Marco Di Francesco
The paper studies how a Follow-the-Leader particle scheme can approximate entropy solutions of a one‑dimensional scalar conservation law when the velocity function is not monotone,…
math.AP2026
The Aronson-Bénilan estimate for a Lagrangian particle discretization of the Porous Medium Equation
Marco Di Francesco, Daniel Matthes
We consider a nearest neighbor, Lagrangian particle discretization of the one dimensional porous medium equation. We prove that the particle model satisfies a discrete analog of th…
math.AP2025
Kermack-McKendrick type models for epidemics with nonlocal aggregation terms
Marco Di Francesco, Fatemeh Ghaderi Zefreh
We propose an approach to model spatial heterogeneity in SIR-type models for the spread of epidemics via \emph{nonlocal aggregation terms}. More precisely, we first consider an SIR…