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

Pages: 311 - 339, Volume 4, Issue 2, June 2005

doi:10.3934/cpaa.2005.4.311       Abstract        Full Text (353.5K)       Related Articles

Y. Goto - NTT Comware, Minato, Tokyo, 108-8019, Japan (email)
K. Ishii - Faculty of Maritime Sciences, Kobe University, Higashinada, Kobe 658-0022, Japan (email)
T. Ogawa - Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan (email)

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.

Keywords:  Motionby mean curvature, Bence-Merrina-Osher algorithm, signed distance function, viscosity solutions.
Mathematics Subject Classification:  35K65,35K55,65M99

Received: March 2003;      Revised: May 2004;      Published: March 2005.