A REACTION-DIFFUSION APPROXIMATION TO AN AREA PRESERVING MEAN CURVATURE FLOW COUPLED WITH A BULK EQUATION

Motivated by the motion of an alcohol droplet, we derive a simplified phenomenological free boundary model which consists of an area preserving mean curvature flow coupled with a bulk equation. Our aim is to introduce a nonlocal reaction-diffusion system with a small parameter epsilon which converges to the original model as epsilon tends to zero. This approximation enables us to overcome the technical difficulty of the free boundary problem arising in the original model.