TY - JOUR
T1 - The Second-Order L 2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane
AU - Lin, Chun Chi
AU - Lue, Yang Kai
AU - Schwetlick, Hartmut R.
N1 - Funding Information:
During working on this project, C.-C. Lin was supported by the National Science Council of Taiwan NSC 101-2115-M-003-002 and the National Center for Theoretical Sciences in Taipei, Taiwan; and Y.-K. Lue was supported by MOST 103-2811-M-003-008. The authors also want to thank the referees for useful comments and corrections toward improving the presentation of this article.
Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.
PY - 2015/4/1
Y1 - 2015/4/1
N2 - 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).
AB - 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).
KW - Elastic energy
KW - Geometric flow
KW - Hinged boundary conditions
KW - Second-order parabolic equation
KW - Willmore functional
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U2 - 10.1007/s10659-015-9518-5
DO - 10.1007/s10659-015-9518-5
M3 - Article
AN - SCOPUS:84939978006
SN - 0374-3535
VL - 119
SP - 263
EP - 291
JO - Journal of Elasticity
JF - Journal of Elasticity
IS - 1-2
ER -