Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

Y. Goto; K. Ishii; T. Ogawa

doi:10.3934/cpaa.2005.4.311

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2005, Volume 4, Issue 2: 311-339. Doi: 10.3934/cpaa.2005.4.311

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Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

1.
NTT Comware, Minato, Tokyo, 108-8019
2.
Faculty of Maritime Sciences, Kobe University, Higashinada, Kobe 658-0022
3.
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578

Received: February 28, 2003

Revised: April 30, 2004

Published: May 2005

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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.

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Mathematics Subject Classification: 35K65,35K55,65M99.

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Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature

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