The employment of nonlocal PDE models to describe biological aggregation and other
phenomena has gained considerable traction in recent years. For cell populations, these …

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 …

We discuss several continuum cell-cell adhesion models based on the underlying
microscopic assumptions. We propose an improvement on these models leading to sharp …

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell
migration during tissue development, homeostasis, and repair, allowing cell populations to …

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 …

We provide a rigorous mathematical framework to establish the limit of a nonlocal model of
cell-cell adhesion system to a local model. When the parameter of the nonlocality goes to 0 …

In recent years, there has been a spike in interest in multiphase tissue growth models.
Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law …

We consider macroscopic descriptions of particles where repulsion is modelled by non-
linear power-law diffusion and attraction by a homogeneous singular kernel leading to …

One of the most fascinating phenomenon observed in reaction diffusion systems is the
emergence of segregated solutions, ie, population densities with disjoint supports. We …

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 …