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Computational studies of non-local anisotropic Allen-Cahn equation. (English) Zbl 1249.35153
Summary: The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by J. Rubinstein and P. Sternberg [IMA J. Appl. Math. 48, No. 3, 249–264 (1992; Zbl 0763.35051)] 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.

35K57 Reaction-diffusion equations
35K65 Degenerate parabolic equations
65N40 Method of lines for boundary value problems involving PDEs
53C80 Applications of global differential geometry to the sciences
Zbl 0763.35051
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