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 …

This paper studies the derivation of the quadratic porous medium equation and a class of
cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a …

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 …

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

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as
cells, tissues and organs coexist and interact across scales to determine both shape and …

Nonlocal cross-diffusion systems on the torus, arising in population dynamics and
neuroscience, are analyzed. The global existence of weak solutions, the weak–strong …

We propose a framework for two-player infinite-dimensional games with cooperative or
competitive structure. These games take the form of coupled partial differential equations in …

We give sharp conditions for global in time existence of gradient flow solutions to a Cahn–
Hilliard‐type equation, with backwards second‐order degenerate diffusion, in any …

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 …

Collective motion of large-scale natural swarms, such as moving animal groups or
expanding bacterial colonies, has been described as self-organized phenomena. Thus, it is …