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A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity

Published online by Cambridge University Press:  12 July 2007

J. Sivaloganathan  and
S. J. Spector
J. Sivaloganathan
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
S. J. Spector
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, IL 629014408, USA
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Abstract

Radial deformations of a ball composed of a nonlinear elastic material and corresponding to cavitation have been much studied. In this paper we use rescalings to show that each such deformation can be used to construct infinitely many non-symmetric singular weak solutions of the equations of nonlinear elasticity for the same displacement boundary-value problem. Surprisingly, this property appears to have been unnoticed in the literature to date.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 4 , August 2002 , pp. 985 - 992
Copyright
Copyright © Royal Society of Edinburgh 2002

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