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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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