Abstract
In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of \(C^{\infty}\)-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):683–698, 1993).
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Lin, CC., Lue, YK., Schwetlick, H.R. (2016). The Second-Order \(L^{2}\)-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane. In: Fosdick, R., Fried, E. (eds) The Mechanics of Ribbons and Möbius Bands. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7300-3_14
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DOI: https://doi.org/10.1007/978-94-017-7300-3_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-7299-0
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