We provide a review of recent advancements in non-local continuous models for migration,
mainly from the perspective of its involvement in embryonal development and cancer …

We study a nonlocal two species cross-interaction model with cross-diffusion. We propose a
positivity preserving finite volume scheme based on the numerical method introduced in [JA …

The repulsion strength at the origin for repulsive/attractive potentials determines the
regularity of local minimizers of the interaction energy. In this paper, we show that if this …

The existence of compactly supported global minimisers for continuum models of particles
interacting through a potential is shown under almost optimal hypotheses. The main …

Motivated by classical vortex blob methods for the Euler equations, we develop a numerical
blob method for the aggregation equation. This provides a counterpoint to existing literature …

This special issue grew out of a BIRS workshop of the same title that was held in February
2012. It contains new research contributions from a broad spectrum of researchers on topics …

We consider a family of interaction functionals consisting of power-law potentials with
attractive and repulsive parts and use the concentration compactness principle to establish …

We study an implicit finite-volume scheme for nonlinear, non-local aggregation-diffusion
equations which exhibit a gradient-flow structure, recently introduced in [R. Bailo, JA Carrillo …

Biological aggregations such as fish schools, bird flocks, bacterial colonies, and insect
swarms have characteristic morphologies governed by the group members' intrinsic social …

We investigate which nonlocal-interaction energies have a ground state (global minimizer).
We consider this question over the space of probability measures and establish a sharp …