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^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

37 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
頁（從 - 到）	6414-6428
頁數	15
期刊	Journal of Differential Equations
卷	252
發行號	12
DOIs	https://doi.org/10.1016/j.jde.2012.03.010
出版狀態	已發佈 - 2012 6月 15

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10.1016/j.jde.2012.03.010

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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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AU - Lin, Chun Chi

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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UR - https://www.scopus.com/pages/publications/84862808540#tab=citedBy

U2 - 10.1016/j.jde.2012.03.010

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M3 - Article

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VL - 252

SP - 6414

EP - 6428

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 12

ER -

L 2-flow of elastic curves with clamped boundary conditions

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L ²-flow of elastic curves with clamped boundary conditions