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A reaction-diffusion approximation to an area preserving mean curvature flow coupled with a bulk equation. (English) Zbl 1207.35189
Summary: 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 $$\varepsilon$$ which converges to the original model as $$\varepsilon$$ tends to zero. This approximation enables us to overcome the technical difficulty of the free boundary problem arising in the original model.

##### MSC:
 35K57 Reaction-diffusion equations 35B25 Singular perturbations in context of PDEs 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 35C20 Asymptotic expansions of solutions to PDEs
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