### Abstract

A new proof of the convergence of the Bence-Merriman-Osher algorithm for the motion of mean curvature is given. The idea is making use of the approximate distance function to the interface and analogous argument in the singular limiting problem for the Allen-Cahn equation via an auxiliary function given by the primitive function of the heat kernel.

Original language | English |
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Pages (from-to) | 311-339 |

Number of pages | 29 |

Journal | Communications on Pure and Applied Analysis |

Volume | 4 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Jun 1 |

### Keywords

- Bence-Merrina-Osher algorithm
- Motion by mean curvature
- Signed distance function
- Viscosity solutions

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Goto, Y., Ishii, K., & Ogawa, T. (2005). Method of the distance function to the Bence-merriman-osher algorithm for motion by mean curvature.

*Communications on Pure and Applied Analysis*,*4*(2), 311-339. https://doi.org/10.3934/cpaa.2005.4.311