From the 1 of 4 linked papers with an AI index.
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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,…
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…
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…
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…