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EVOLUTION OF SPIRAL-SHAPED POLYGONAL CURVE BY CRYSTALLINE CURVATURE FLOW WITH A PINNED TIP

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84241

Title: EVOLUTION OF SPIRAL-SHAPED POLYGONAL CURVE BY CRYSTALLINE CURVATURE FLOW WITH A PINNED TIP
Authors: Ishiwata ,Tetsuya Browse this author
Ohtsuka, Takeshi Browse this author
Keywords: Crystalline eikonal-curvature flow
Evolution of convex polygonal spiral
Issue Date: 18-Nov-2016
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1097
Start Page: 1
End Page: 31
Abstract: Evolution of convex polygonal spiral with fixed center by crystalline eikonal-curvature flow is considered. In this evolution we consider a new facet of the polygonal curve generates from center when a facet associated with the center evolves with enough length, which is equal to the length of the facet in Wulff shape of energy density function. We prove the existence, uniqueness and intersection free of solution to our formulation globally-in-time. In the proof of the existence we also prove that new facets are generated repeatedly in time. The important property for intersection-free result is monotonicity property such that the normal velocity of every facets are positive after the next new facet is generated, so that the center is always behind of the moving facets.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69901
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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