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GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

Published online by Cambridge University Press:  27 September 2012

SATOSHI KAWAKUBO*
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan (email: kawakubo@math.sci.fukuoka-u.ac.jp)
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Abstract

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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.

Type
Research Article
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

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