Tetsuya Ishiwata, Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570, Japan, e-mail: tisiwata@shibaura-it.ac.jp
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.
Keywords: curvature driven motion; crystalline curvature; spiral growth
Classification (MSC 2010): 34A34, 39A12, 74N05
Full text available as PDF.
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
