24 citations · 28 across the 11 of their papers we have counts for
11 papers
Competing effects in fourth-order aggregation-diffusion equations
José Antonio Carrillo, Antonio Esposito, Carles Falcó +1
We give sharp conditions for global in time existence of gradient flow solutions to a Cahn-Hilliard-type equation, with backwards second order degenerate diffusion, in any dimensio…
Graph-to-local limit for a multi-species nonlocal cross-interaction system
Antonio Esposito, Georg Heinze, Jan-Frederik Pietschmann +1
In this note we continue the study of nonlocal interaction dynamics on a sequence of infinite graphs, extending the results of [Esposito et. al 2023+] to an arbitrary number of spe…
Graph-to-local limit for the nonlocal interaction equation
Antonio Esposito, Georg Heinze, André Schlichting
We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Ou…
Nonlocal approximation of nonlinear diffusion equations
José Antonio Carrillo, Antonio Esposito, Jeremy Sheung-Him Wu
We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are…
Porous medium equation and cross-diffusion systems as limit of nonlocal interaction
Martin Burger, Antonio Esposito
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a…
On a novel gradient flow structure for the aggregation equation
A. Esposito, R. S. Gvalani, A. Schlichting +1
The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction ene…