curvature driven motion; crystalline curvature; spiral growth
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.
 Gurtin, M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane
. Oxford Mathematical Monographs Clarendon Press, Oxford (1993). MR 1402243
| Zbl 0787.73004