On local uniqueness in nonlinear elastodynamics

Knops, R.

doi:10.1090/S0033-569X-06-01023-7

Author: R. J. Knops
Journal: Quart. Appl. Math. 64 (2006), 321-333
MSC (2000): Primary 74B20; Secondary 74H25
DOI: https://doi.org/10.1090/S0033-569X-06-01023-7
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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