Ishiwata, Tetsuya Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion. (English) Zbl 1349.34040 Math. Bohem. 140, No. 2, 111-119 (2015). Summary: 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. Cited in 1 Review MSC: 34A34 Nonlinear ordinary differential equations and systems 53A04 Curves in Euclidean and related spaces 82D25 Statistical mechanics of crystals Keywords:curvature driven motion; crystalline curvature; spiral growth × Cite Format Result Cite Review PDF Full Text: DOI Link