Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion

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Abstract

We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never occurs. Finally, we show that spiral-shaped solutions exist globally in time.

Original languageEnglish
Article numberA111
Pages (from-to)111-119
Number of pages9
JournalMathematica Bohemica
Volume140
Issue number2
Publication statusPublished - 2015

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Keywords

  • Crystalline curvature
  • Curvature driven motion
  • Spiral growth

ASJC Scopus subject areas

  • Mathematics(all)

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