3 papers
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.AP2024
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…
math.AP2008
Singular convergence of nonlinear hyperbolic chemotaxis systems to Keller--Segel type models
M. Di Francesco, D. Donatelli
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximatin…