Abstract
In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C∞-smooth solutions during the evolution, given the initial curves that are only C2-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):683–698, 1993).
Original language | English |
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Pages (from-to) | 263-291 |
Number of pages | 29 |
Journal | Journal of Elasticity |
Volume | 119 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2015 Apr 1 |
Keywords
- Elastic energy
- Geometric flow
- Hinged boundary conditions
- Second-order parabolic equation
- Willmore functional
ASJC Scopus subject areas
- General Materials Science
- Mechanics of Materials
- Mechanical Engineering