Diffuse-interface treatment of the anisotropic mean-curvature flow. (English) Zbl 1099.53044

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.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
80A22 Stefan problems, phase changes, etc.
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