Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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] Morton E. Gurtin and Scott J. Spector, On stability and uniqueness in finite elasticity, Arch. Rational Mech. Anal. 70 (1979), no. 2, 153–165. MR 546633, https://doi.org/10.1007/BF00250352
  • [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] Scott J. Spector, On uniqueness in finite elasticity with general loading, J. Elasticity 10 (1980), no. 2, 145–161 (English, with French summary). MR 576164, https://doi.org/10.1007/BF00044500
  • [5] S. J. Spector, On uniqueness for the traction problem in finite elasticity, in preparation
  • [6] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. 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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