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Applications of Mathematics

, Volume 48, Issue 6, pp 437–453 | Cite as

Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow

  • Michal Beneš
Article

Abstract

We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.

mean-curvature flow phase-field method FDM Finsler geometry 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2003

Authors and Affiliations

  • Michal Beneš
    • 1
  1. 1.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePrague 2Czech Republic

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