A modified phase field approximation for mean curvature flow with conservation of the volume

Abstract

This paper is concerned with the motion of a time dependent hypersurface ∂Ω(t) in R that evolves with a normal velocity Vn = κ− ∂Ω(t) κ dσ, where κ is the mean curvature of ∂Ω(t), and I stands for 1 |I| I . Phase field approximation of this motion leads to the nonlocal Allen–Cahn equation ∂tu = ∆u− 1 ǫ2 W (u) + 1 ǫ2 Q W (u) dx, where Q is an open box of R… (More)

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Cite this paper

@inproceedings{Bretin2009AMP, title={A modified phase field approximation for mean curvature flow with conservation of the volume}, author={Elie Bretin}, year={2009} }