The Second-Order L 2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane
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- 作者：Chun-Chi Lin ; Yang-Kai Lue ; Hartmut R. Schwetlick
- 关键词：Geometric flow ; Second ; order parabolic equation ; Hinged boundary conditions ; Elastic energy ; Willmore functional ; 35B65 ; 35K51 ; 53A04 ; 53C44
- 刊名：Journal of Elasticity
- 出版年：2015
- 出版时间：April 2015
- 年：2015
- 卷：119
- 期：1-2
- 页码：263-291
- 全文大小：956 KB
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- 刊物主题：Physics
Mechanics
Automotive and Aerospace Engineering and Traffic - 出版者：Springer Netherlands
- ISSN：1573-2681
文摘
In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C ?/sup>-smooth solutions during the evolution, given the initial curves that are only C 2-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683-98, 1993).