MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 677-684, 2014

Computational studies of conserved mean-curvature flow

Miroslav Kolář, Michal Beneš, Daniel Ševcovič

Miroslav Kolář, Michal Beneš, Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic, e-mail: kolarmir@fjfi.cvut.cz, michal.benes@fjfi.cvut.cz; Daniel Ševcovič, Comenius University, Faculty of Mathematics and Physics, Institute of Applied Mathematics, Mlynská dolina 15, 842 48 Bratislava, Slovakia, e-mail: sevcovic@fmph.uniba.sk

Abstract: 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.

Keywords: phase transitions; area-preserving mean-curvature flow; parametric method

Classification (MSC 2010): 35K57, 35K65, 65N40, 53C80


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