Nonlocal to Local convergence to model cell–cell Adhesion

In biology, cell–cell adhesion can be modeled at different scales, starting from a particle system where particles interact through nonlocal forces. The empirical measure of this system satisfies a nonlocal evolution equation. In the limit where the interaction length (that is the nonlocality) tends to zero, the model converges formally to a local fourth-order PDE. In this talk, I will show that this result can be made rigorous analytically and is supported by numerical simulations.