The aim of this survey is to serve as an introduction to the different techniques available in
the broad field of aggregation-diffusion equations. We aim to provide historical context, key …

Nonlocal advection is a key process in a range of biological systems, from cells within
individuals to the movement of whole organisms. Consequently, in recent years, there has …

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 …

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 …

We establish uniqueness of vanishing radially decreasing entire solutions, which we call
ground states, to some semilinear fractional elliptic equations. In particular, we treat the …

Consider a collection of particles interacting through an attractive-repulsive potential given
as a difference of power laws and normalized so that its unique minimum occurs at unit …

The existence and non-uniqueness of stationary distributions for distribution dependent
stochastic differential equations with regular coefficients and singular coefficients are …

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 …

Particles interacting through long-range attraction and short-range repulsion given by power-
laws have been widely used to model physical and biological systems and to predict or …

We consider a generalised Keller–Segel model with non-linear porous medium type
diffusion and non-local attractive power law interaction, focusing on potentials that are more …