American Institute of Mathematical Sciences

October  2015, 8(5): 881-888. doi: 10.3934/dcdss.2015.8.881

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

 1 Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570

Received  January 2014 Revised  March 2015 Published  July 2015

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 flow 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 solutions.
Citation: Tetsuya Ishiwata. On spiral solutions to generalized crystalline motion with a rotating tip motion. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 881-888. doi: 10.3934/dcdss.2015.8.881
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References:
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