Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow |
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Authors: | Michal Beneš |
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Institution: | (1) Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague 2, Czech Republic |
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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. |
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Keywords: | mean-curvature flow phase-field method FDM Finsler geometry |
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