93 citations · 214 across the 12 of their papers we have counts for
9 papers · 1 filter
Well-posedness of an interaction model on Riemannian manifolds
Razvan C. Fetecau, Francesco S. Patacchini
We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posednes…
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini, Dejan Slepčev
We study the approximation of the nonlocal-interaction equation restricted to a compact manifold embedded in , and more generally compact sets with posi…
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…
Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour
Mikaela Iacobelli, Francesco Patacchini, Filippo Santambrogio
In this paper we devote our attention to a class of weighted ultrafast diffusion equations arising from the problem of quantisation for probability measures. These equations have a…
Existence of ground states for aggregation-diffusion equations
J. A. Carrillo, M. G. Delgadino, F. S. Patacchini
We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of t…
A blob method for diffusion
José Antonio Carrillo, Katy Craig, Francesco S. Patacchini
As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, determinis…
Discrete minimisers are close to continuum minimisers for the interaction energy
J. A. Cañizo, F. S. Patacchini
Under suitable technical conditions we show that minimisers of the discrete interaction energy for attractive-repulsive potentials converge to minimisers of the corresponding conti…
Geometry of minimizers for the interaction energy with mildly repulsive potentials
J. A. Carrillo, A. Figalli, F. S. Patacchini
We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class and mildly repulsive at t…
Existence of Compactly Supported Global Minimisers for the Interaction Energy
J. A. Cañizo, J. A. Carrillo, F. S. Patacchini
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumpti…