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

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 …

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 …

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 develop structure preserving schemes for a class of nonlinear mobility continuity
equation. When the mobility is a concave function, this equation admits a form of gradient …

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 …

There has been recently an important interest in deriving rigorously the Cahn-Hilliard
equation from the nonlocal equation, also called aggregation equation. So far, only non …

We consider aggregation-diffusion equations with merely bounded nonlocal interaction
potential $ K $. We are interested in establishing their well-posedness theory when the …

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 …

Formation of organs and specialized tissues in embryonic development requires migration
of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here …