GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS
2012 ◽
Vol 88
(1)
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pp. 70-80
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AbstractThe 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.
2005 ◽
Vol 15
(03)
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pp. 871-890
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2007 ◽
Vol 330
(2)
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pp. 1139-1151
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2014 ◽
Vol 76
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pp. 158-168
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2006 ◽
Vol 43
(7-8)
◽
pp. 854-869
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2003 ◽
Vol 2003
(9)
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pp. 539-547
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Keyword(s):
Keyword(s):