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

This paper is concerned with the motion of a time‐dependent hypersurface ∂Ω(t) in ℝd that evolves with a normal velocity where κ is the mean curvature of ∂Ω(t), and g is an external forcing term. Phase field approximation of this motion leads to the Allen–Cahn equation where ε is an approximation pa...

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