L 2-flow of elastic curves with clamped boundary conditions

Chun Chi Lin

doi:10.1016/j.jde.2012.03.010

L ²-flow of elastic curves with clamped boundary conditions

Chun Chi Lin^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

In this paper we investigate the L ²-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L ²-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.

Original language	English
Pages (from-to)	6414-6428
Number of pages	15
Journal	Journal of Differential Equations
Volume	252
Issue number	12
DOIs	https://doi.org/10.1016/j.jde.2012.03.010
Publication status	Published - 2012 Jun 15

Keywords

Clamped boundary condition
Elastic curve
Fourth-order flow

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2012.03.010

Cite this

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title = "L 2-flow of elastic curves with clamped boundary conditions",

abstract = "In this paper we investigate the L 2-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L 2-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.",

keywords = "Clamped boundary condition, Elastic curve, Fourth-order flow",

author = "Lin, \{Chun Chi\}",

note = "Funding Information: This work was sponsored by Taiwan National Science Council Grant 98-2115-M-003-011-MY2 and partially supported by National Center for Theoretical Sciences in Taiwan. The author would like to thank the referee for valuable comments and Simon Morgan for his great help in revising this article.",

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N1 - Funding Information: This work was sponsored by Taiwan National Science Council Grant 98-2115-M-003-011-MY2 and partially supported by National Center for Theoretical Sciences in Taiwan. The author would like to thank the referee for valuable comments and Simon Morgan for his great help in revising this article.

PY - 2012/6/15

Y1 - 2012/6/15

N2 - In this paper we investigate the L 2-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L 2-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.

AB - In this paper we investigate the L 2-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L 2-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.

KW - Clamped boundary condition

KW - Elastic curve

KW - Fourth-order flow

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