Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On local uniqueness in nonlinear elastodynamics

Author: R. J. Knops
Journal: Quart. Appl. Math. 64 (2006), 321-333
MSC (2000): Primary 74B20; Secondary 74H25
Published electronically: May 3, 2006
MathSciNet review: 2243866
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Abstract: A conservation law, derived from properties of the energy-momentum tensor, is used to establish uniqueness of suitably constrained solutions to the initial boundary value problem of nonlinear elastodynamics. It is assumed that the region is star-shaped, that the data are affine, and that the strain-energy function is strictly rank-one convex and quasi-convex. It is shown how these assumptions may be successively relaxed provided that the class of considered solutions is correspondingly further constrained.

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Additional Information

R. J. Knops
Affiliation: School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, U.K.

DOI: https://doi.org/10.1090/S0033-569X-06-01023-7
Keywords: Nonlinear elastodynamics, uniqueness, constrained solutions
Received by editor(s): July 25, 2005
Published electronically: May 3, 2006
Article copyright: © Copyright 2006 Brown University

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