A reaction-diffusion approximation to an area preserving mean curvature flow coupled with a bulk equation
Résumé
Motivated by the motion of an alcohol droplet, we derive a simpli- fied 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 ε which converges to the original model as ε tends to zero. This approximation enables us to overcome the technical difficulty of the free boundary problem arising in the original model.