Geodesic
Computational studies of non-local anisotropic Allen-Cahn equation
Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 429-437

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The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.
The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.
DOI : 10.21136/MB.2011.141702
Classification : 35K57, 35K65, 53C80, 65N40
Keywords: Allen-Cahn equation; phase transitions; mean-curvature flow; finite-difference method 
Beneš, Michal; Yazaki, Shigetoshi; Kimura, Masato. Computational studies of non-local anisotropic Allen-Cahn equation. Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 429-437. doi: 10.21136/MB.2011.141702
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