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math.AP2020
Many-particle limit for a system of interaction equations driven by Newtonian potentials
Marco Di Francesco, Antonio Esposito, Markus Schmidtchen
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and a…
math.AP2019
Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit
Antonio Esposito, Francesco S. Patacchini, André Schlichting +1
We consider dynamics driven by interaction energies on graphs. We introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with…
math.AP2017
Nonlinear degenerate cross-diffusion systems with nonlocal interaction
M. Di Francesco, A. Esposito, S. Fagioli
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sc…