Given a large ensemble of interacting particles, driven by nonlocal interactions and localized
repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial differential …

Combining the classical theory of optimal transport with modern operator splitting
techniques, we develop a new numerical method for nonlinear, nonlocal partial differential …

In this work we study a tissue growth model with applications to tumour growth. The model is
based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the …

For the interaction energy with repulsive–attractive potentials, we give generic conditions
which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein …

As a counterpoint to classical stochastic particle methods for linear diffusion equations, such
as Langevin dynamics for the Fokker-Planck equation, we develop a deterministic particle …

We complete previous results about the incompressible limit of both the n-dimensional (n≥
3) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous …

Motivated by recent work on approximation of diffusion equations by deterministic interacting
particle systems, we develop a nonlocal approximation for a range of linear and nonlinear …

We consider a nonlocal aggregation equation with degenerate diffusion, which describes
the mean‐field limit of interacting particles driven by nonlocal interactions and localized …

We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in
the Wasserstein space of a functional with competing attractive-repulsive interactions. We …

This chapter reviews (and expands) some recent results on the modeling of aggregation-
diffusion phenomena at various scales, focusing on the emergence of collective dynamics …