Article
MSC:
35A40,
53C44,
80A22,
82C26 | MR 2025297 | Zbl 1099.53044 | DOI: 10.1023/B:APOM.0000024485.24886.b9
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Keywords:
mean-curvature flow; phase-field method; FDM; Finsler geometry
mean-curvature flow; phase-field method; FDM; Finsler geometry
Summary:
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.
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