On the motion of polygonal curves with asymptotic lines
by crystalline curvature flow with bulk effect
Tetsuya Ishiwata - Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570, Japan (email)
Abstract: The behavior of polygonal curves with asymptotic lines to crystalline motion with the bulk effect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.
Keywords: Crystalline motion, Crystalline curvature,
Received: September 2009; Revised: November 2009; Published: November 2010.