# American Institute of Mathematical Sciences

February  2011, 4(1): 125-154. doi: 10.3934/dcdss.2011.4.125

## A reaction-diffusion approximation to an area preserving mean curvature flow coupled with a bulk equation

 1 CMI, Université de Provence, 39 rue Frédéric Joliot-Curie 13453 Marseille cedex 13, France 2 CNRS and Laboratoire de Mathématiques, Université de Paris-Sud 11, F-91405 Orsay Cedex, France 3 Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1 Higashi Mita, Tama-ku, Kawasaki, 214-8571, Japan

Received  March 2009 Revised  December 2009 Published  October 2010

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 $\e$ which converges to the original model as $\e$ tends to zero. This approximation enables us to overcome the technical difficulty of the free boundary problem arising in the original model.
Citation: Marie Henry, Danielle Hilhorst, Masayasu Mimura. A reaction-diffusion approximation to an area preserving mean curvature flow coupled with a bulk equation. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 125-154. doi: 10.3934/dcdss.2011.4.125
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