Special Session 85: Phase-field models and their singular limits

Deterministic particle approximation of a fourth-order PDE
Charles Elbar
Universite Claude Bernard Lyon 1
France
Co-Author(s):    Alejandro Fernandez-Jimenez
Abstract:
Many partial differential equations describe how a macroscopic density of particles/cells evolves in time. So, it is a natural question to ask whether there is a microscopic (deterministic) model that leads to a given macroscopic PDE. For second-order aggregation-diffusion equations, this connection has been proved, starting with the porous medium equation in 2001. In this work, we extend that framework to a fourth-order equation, inspired by applications in cell-cell adhesion in biological systems. This is a joint work with Alejandro Fernandez-Jimenez.