Michal Beneš, Czech Technical University in Prague, Praha, Czech Republic, e-mail: michal.benes@fjfi.cvut.cz; Shigetoshi Yazaki, University of Miyazaki, Miyazaki, Japan, e-mail: yazaki@cc.miyazaki-u.ac.jp; Masato Kimura, Kyushu University, Fukuoka, Japan, e-mail: masato@math.kyushu-u.ac.jp
Abstract: 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.
Keywords: Allen-Cahn equation, phase transitions, mean-curvature flow, finite-difference method
Classification (MSC 2010): 35K57, 35K65, 65N40, 53C80
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