316 citations · 2.6k across the 149 of their papers we have counts for
13 papers · 1 filter
The geometry of diffusing and self-attracting particles in a one-dimensional fair-competition regime
Vincent Calvez, Jose Antonio Carrillo, Franca Hoffmann
We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and…
Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime
José A. Carrillo, Yoshie Sugiyama
We first show the existence of unique global minimizer of the free energy for all masses associated to a nonlinear diffusion version of the classical Keller-Segel model when the di…
Displacement convexity for the entropy in semidiscrete nonlinear Fokker-Planck equations
José A. Carrillo, Ansgar Jüngel, Matheus C. Santos
The displacement -convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constan…
Equilibria of homogeneous functionals in the fair-competition regime
Vincent Calvez, Jose Antonio Carrillo, Franca Hoffmann
We consider macroscopic descriptions of particles where repulsion is modelled by non-linear power-law diffusion and attraction by a homogeneous singular/smooth kernel leading to va…
Sharp conditions to avoid collisions in singular Cucker-Smale interactions
Jose A. Carrillo, Young-Pil Choi, Piotr B. Mucha +1
We consider the Cucker-Smale flocking model with a singular communication weight with . We provide a critical value of the exponent in the communication w…
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…