Geodesic
Computational studies of conserved mean-curvature flow
Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 677-684

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The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are presented as well.
DOI : 10.21136/MB.2014.144144
Classification : 35K57, 35K65, 53C80, 65N40
Keywords: phase transitions; area-preserving mean-curvature flow; parametric method 
Kolář, Miroslav; Beneš, Michal; Ševčovič, Daniel. Computational studies of conserved mean-curvature flow. Mathematica Bohemica, Tome 139 (2014) no. 4, pp. 677-684. doi: 10.21136/MB.2014.144144
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