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

2009/04/01 by Élie Bretin, Bretin, Elie, Morgan Brassel +1
Materials Science · #35K57 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.0904.0098

openalex publication_date 2009/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the motion of a time dependent hypersurface that evolves by mean curvature flow with a a volume constraint. Phase field approximation of this motion leads to the well known nonlocal Allen--Cahn equation. Here we propose a modified version of this equation, and we show that it has better volume preserving properties than the classical one, even in the presence of an additional forcing term.

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