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Hokkaido University Preprint Series in Mathematics >
EVOLUTION OF SPIRAL-SHAPED POLYGONAL CURVE BY CRYSTALLINE CURVATURE FLOW WITH A PINNED TIP
| 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
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Submitter: 数学紀要登録作業用
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