Motion of polygonal curved fronts by crystalline motion: v-shaped solutions and eventual monotonicity

Pages: 717 - 726, Issue Special, September 2011

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Tetsuya Ishiwata - Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570, Japan (email)

Abstract: This paper deals with behavior of polygonal plane curves with two asymptotic lines by generalized crystalline curvature flow with a driving force. We show global existence of V-shaped solutions and investigate the deformation patterns of non-V-shaped solutions. We also show that non-V-shaped solutions become V-shaped in finite time.

Keywords:  Motion by crystalline curvature, polygonal curves, eventual monotonicity
Mathematics Subject Classification:  Primary: 34A34, 39A12, 74N05, ; Secondary: 53A04, 34A26.

Received: May 2010;      Revised: July 2011;      Published: October 2011.