Abstract

We consider a model for cell polarization given by a nonlocal reaction-diffusion system on a two-dimensional surface. We prove the convergence to a free boundary problem in a fast reaction limit and derive conditions for the onset of polarization. Furthermore we study regularity properties of the nonlocal parabolic obstacle problem that represents the asymptotic reduction.

(This is joint work with Anna Logioti, Barbara Niethammer and Juan Velazquez.)