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

Marie Henry (1) , Danielle Hilhorst (2) , Masayasu Mimura (3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 Meiji university

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.

Mots clés: reaction-diffusion system of conservative type; singular limits; non local motion by mean curvature; asymptotic expansions

Domaines: Equations aux dérivées partielles [math.AP]

Marie Henry, Danielle Hilhorst, Masayasu Mimura. A reaction-diffusion approximation to an area preserving mean curvature flow coupled with a bulk equation. Discrete and Continuous Dynamical Systems - Series A, 2011, 4 (1), pp.125-154. ⟨10.3934/dcdss.2011.4.125⟩. ⟨hal-01308262⟩