Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On continuous dependence in finite elasticity

Author: Scott J. Spector
Journal: Quart. Appl. Math. 38 (1980), 135-138
MSC: Primary 73G05
DOI: https://doi.org/10.1090/qam/575837
MathSciNet review: 575837
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Abstract: We investigate the relation between stability and continuous dependence for a nonlinearly elastic body at equilibrium. We show that solutions of the governing equations that lie in a convex, stable set of deformations depend continuously on the body forces and the surface tractions. The definition of stability used is essentially due to Hadamard.

References [Enhancements On Off] (What's this?)

  • [1] M. E. Gurtin and S. J. Spector, On stability and uniqueness in finite elasticity, Arch. Rat. Mech. Anal., to appear MR 546633
  • [2] G. Fichera, Existence theorems in elasticity, in Handbuch der Physik, VIa/2, Berlin, Springer-Verlag (1972)
  • [3] J. Hadamard, Leçons sur la propagation des ondes et les equations d'hydrodynamique, Paris, Hermann (1903)
  • [4] S. J. Spector, On uniqueness in finite elasticity with general loading, J. Elasticity, to appear MR 576164
  • [5] S. J. Spector, On uniqueness for the traction problem in finite elasticity, in preparation
  • [6] R. A. Adams, Sobolev spaces, New York, Academic Press (1975) MR 0450957

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DOI: https://doi.org/10.1090/qam/575837
Article copyright: © Copyright 1980 American Mathematical Society

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