On continuous dependence in finite elasticity

Spector, Scott J.

doi:10.1090/qam/575837

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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, DOI https://doi.org/10.1007/BF00250352

G. Fichera, Existence theorems in elasticity, in Handbuch der Physik, VIa/2, Berlin, Springer-Verlag (1972)

J. Hadamard, Leçons sur la propagation des ondes et les equations d’hydrodynamique, Paris, Hermann (1903)

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, DOI https://doi.org/10.1007/BF00044500

S. J. Spector, On uniqueness for the traction problem in finite elasticity, in preparation

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