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June 2001 Point-extinction and geometric expansion of solutions to a crystalline motion
Shigetoshi YAZAKI
Hokkaido Math. J. 30(2): 327-357 (June 2001). DOI: 10.14492/hokmj/1350911957


We consider the asymptotic behavior of solutions to a generalized crystalline motion which describes evolution of plane curves driven by nonsmooth interfacial energy. Our main results say that solution polygonal curves expand to infinity or shrink to a single point depending on the size of initial data and the sign of the driving force term. In the expanding case, we show that any rescaled solution polygon converges to the boundary of the Wulff shape for the driving force term and hence if the driving force term is a constant, then any solution polygon approaches to an expanding regular polygon even if the motion is anisotropic. We also give lower and upper bounds of the extinction time for the shrinking case. In the appendix, we shall explain the notion of a discrete curvature and crystalline curvature from a numerical point of view.


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Shigetoshi YAZAKI. "Point-extinction and geometric expansion of solutions to a crystalline motion." Hokkaido Math. J. 30 (2) 327 - 357, June 2001.


Published: June 2001
First available in Project Euclid: 22 October 2012

zbMATH: 1192.82077
MathSciNet: MR1844823
Digital Object Identifier: 10.14492/hokmj/1350911957

Primary: 58F25
Secondary: 34A26, 34A34, 53A04, 73B30, 82D25

Rights: Copyright © 2001 Hokkaido University, Department of Mathematics


Vol.30 • No. 2 • June 2001
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