Geodesic
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 111-119.

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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.
DOI : 10.21136/MB.2015.144318
Classification : 34A26, 34A34, 39A12, 74N05, 82D25
Keywords: curvature driven motion; crystalline curvature; spiral growth 
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Ishiwata, Tetsuya. Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion. Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 111-119. doi : 10.21136/MB.2015.144318. http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144318/

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