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Computational studies of conserved mean-curvature flow. (English) Zbl 1349.65374
Summary: 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.

MSC:
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C80 Applications of global differential geometry to the sciences
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