Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature

Shigetoshi Yazaki

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 903-912
  • ISSN: 0023-5954

Abstract

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Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.

How to cite

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Yazaki, Shigetoshi. "Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature." Kybernetika 43.6 (2007): 903-912. <http://eudml.org/doc/33906>.

@article{Yazaki2007,
abstract = {Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.},
author = {Yazaki, Shigetoshi},
journal = {Kybernetika},
keywords = {essentially admissible polygon; crystalline curvature; the Wulff shape; isoperimetric inequality; essentially admissible polygon; crystalline curvature; the Wulff shape; isoperimetric inequality},
language = {eng},
number = {6},
pages = {903-912},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature},
url = {http://eudml.org/doc/33906},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Yazaki, Shigetoshi
TI - Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 903
EP - 912
AB - Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.
LA - eng
KW - essentially admissible polygon; crystalline curvature; the Wulff shape; isoperimetric inequality; essentially admissible polygon; crystalline curvature; the Wulff shape; isoperimetric inequality
UR - http://eudml.org/doc/33906
ER -

References

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  9. Taylor J. E., Motion of curves by crystalline curvature, including triple junctions and boundary points, Diff. Geom.: partial diff. eqs. on manifolds (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., 54 (1993), Part I, 417–438, AMS, Providence (1990) MR1216599
  10. Taylor J. E., Cahn, J., Handwerker C., 10.1016/0956-7151(92)90090-2, Acta Metall. 40 (1992), 1443–1474 (1992) DOI10.1016/0956-7151(92)90090-2
  11. Yazaki S., 10.1007/s005260100094, Calc. Var. 14 (2002), 85–105 Zbl1143.37320MR1883601DOI10.1007/s005260100094
  12. Yazaki S., On an anisotropic area-preserving crystalline motion and motion of nonadmissible polygons by crystalline curvature, Sūrikaisekikenkyūsho Kōkyūroku 1356 (2004), 44–58 
  13. Yazaki S., 10.2977/prims/1199403812, Publ. Res. Inst. Math. Sci. 43 (2007), 155–170 Zbl1132.53036MR2317117DOI10.2977/prims/1199403812

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