Global solutions of the equation of the Kirchhoff elastic rod in space forms

Authors

  • S. Kawakubo Fukuoka University

Keywords:

Kirchhoff elastic rods, calculus of variations, ordinary differential equations, initial-value problems, global solutions

Abstract

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. 10.1017/S0004972712000767

Author Biography

S. Kawakubo, Fukuoka University

Department of Applied Mathematics, Assistant Professor

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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