Nonlocal models of cell-cell adhesion and their Cahn-Hilliard approximation

Speaker:  Carles Falcó (University of Oxford)
Date:  Thursday, 16 March 2023 - 12:30
Place:  Aula Naranja, ICMAT


Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue
development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes.
Adhesive forces are highly linked to the cell geometry and often, continuum models represent these by nonlocal attractive interactions.

In this talk, I will explain how such models can be approximated by Cahn-Hilliard type equations in the limit of short-range interactions.
The resulting model is a local aggregation-diffusion equation, resembling a thin-film type equation, and numerical simulations in one
and two dimensions reveal that it still shows the diversity of patterns observed both in experiments and in previously used nonlocal models.

Finally, I will discuss some recent work studying existence of solutions for the local model.