Special Session 157: Advances in PDE-Based and Data-Driven Approaches for Applied Sciences

A mathematical model of phase separation on biomembranes
Maurizio Grasselli
Politecnico di Milano
Italy
Co-Author(s):    D. Caetano, C.M. Elliott, A. Poiatti
Abstract:
We present a model for phase separation of multiple components on a biological membrane, allowing for small deformations of a spherical shape. The model couples a multi-component Cahn--Hilliard equation with an equation for the membrane geometry, derived using variational principles. We show that the system is well posed and that solutions become regular over time, staying away from pure phases. Moreover, every solution eventually converges to a single equilibrium configuration.