Geodesic
Diffuse-interface treatment of the anisotropic mean-curvature flow
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 437-453.

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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.
DOI : 10.1023/B:APOM.0000024485.24886.b9
Classification : 35A40, 53C44, 80A22, 82C26
Keywords: mean-curvature flow; phase-field method; FDM; Finsler geometry 
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     title = {Diffuse-interface treatment of the anisotropic mean-curvature flow},
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Beneš, Michal. Diffuse-interface treatment of the anisotropic mean-curvature flow. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 437-453. doi : 10.1023/B:APOM.0000024485.24886.b9. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024485.24886.b9/

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