On spiral solutions to generalized crystalline motion with a rotating tip motion

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In our previous paper we proposed a crystalline motion of spiral- shaped polygonal curves with a tip motion as a simple model of a step motion on a crystal surface under screw dislocation and discussed global existence of spiral solutions to the proposed model. In this paper we extend the previous results for generalized crystalline curvature ow with a suitable tip motion. We show that solution curves never intersect a trajectory of a tip and has no self-intersections. We also show that any facet never disappear during time evolution. Finally we show a time-global existence of the spiral-shaped solu- tions.

Original languageEnglish
Pages (from-to)881-888
Number of pages8
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number5
Publication statusPublished - 2015 Oct 1



  • Crystalline curvature
  • Motion by curvature
  • Polygonal curves
  • Spirals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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