American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 717-726. doi: 10.3934/proc.2011.2011.717

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

Tetsuya Ishiwata 1,

1. 

Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570, Japan

Received  May 2010 Revised  July 2011 Published  October 2011

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, 34A2.
Citation: Tetsuya Ishiwata. Motion of polygonal curved fronts by crystalline motion: v-shaped solutions and eventual monotonicity. Conference Publications, 2011, 2011 (Special) : 717-726. doi: 10.3934/proc.2011.2011.717
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