Global solutions of the equation of the Kirchhoff elastic rod in space forms
Global solutions of the equation of the Kirchhoff elastic rod in space forms
复制标题
基尔霍夫弹性杆方程空间形式的全局解
DOI：
10.1017/s0004972712000767
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Satoshi Kawakubo
中科院分区：
文献类型：
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作者：
田中 真紀子;Peter Quast;Makoto Ozawa;Makoto Ozawa;伊藤仁一;Satoshi Kawakubo
Kirchhoff弹性杆是弹性细杆平衡构形的数学模型之一，定义为与弯曲和扭转效应有关的能量的Euler-Lagrange方程的解。本文考虑空间形式的Kirchhoff弹性杆。特别地，我们给出了Euler-Lagrange方程初值问题整体解的存在唯一性。这意味着任意有限长的克希霍夫弹性杆可以延伸到无限长。
The Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler–Lagrange equations associated to the energy with the effect of bending and twisting. In this paper, we consider Kirchhoff elastic rods in a space form. In particular, we give the existence and uniqueness of global solutions of the initial-value problem for the Euler–Lagrange equations. This implies that an arbitrary Kirchhoff elastic rod of finite length extends to that of infinite length.