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Implications Of Hadamard's Conditions For Elastic Stability With Respect To Uniqueness Theorems

Published online by Cambridge University Press:  20 November 2018

J. L. Ericksen  and
R. A. Toupin
J. L. Ericksen
Affiliation:
Applied Mathematics Branch, Naval Research Laboratory, Washington, D.C
R. A. Toupin
Affiliation:
Applied Mathematics Branch, Naval Research Laboratory, Washington, D.C
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Introduction. The purpose of this paper is to discuss implications of Hadamard's condition for elastic stability (2, §269) with respect to uniqueness of solutions of boundary value problems in the theory of small deformations superimposed on large. We show that a slightly refined form of his condition implies a uniqueness theorem for displacement boundary value problems. We construct a counter-example showing that his condition does not imply uniqueness of solutions for one type of stress boundary value problem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 432 - 436
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Green, A. E., Rivlin, R. S., and Shield, R. T., General theory of small elastic deformations superposed on finite elastic deformations, Proc. Roy. Soc. London (A), 211 (1951), 128–154.Google Scholar
2. Hadamard, J., Leçons sur la propagation des ondes et les équations de l'hydrodynamique (Paris, 1903).Google Scholar
3. Kellogg, O. D., Foundations of Potential Theory (New York, 1929).Google Scholar
4. Kirchhoff, G., Ueber die Gleichungen des Gleichgewichts eines elastischen Körpers bei nicht unendlich kleinen Verschiebungen seiner Theile, Akad. Wiss. Wien Sitz., 9 (1852), 762–773.Google Scholar
5. Thomson, W. (Lord Kelvin), On the reflexion and refraction of light, Phil. Mag., 26 (1888), 414–425.Google Scholar
6. Truesdell, C., The mechanical foundations of elasticity and fluid dynamics, J. Rational Mech. Anal., 1 (1952), 125–300.Google Scholar
7. Truesdell, C., The Kinematics of Vorticity (Bloomington, 1954).Google Scholar
8. Truesdell, C., Das ungelöste Hauptproblem der endlichen Elastizitätstheorie, to appear in Z.a.M.M.Google Scholar
9. Whittaker, E., A History of the Theories of Aether and Electricity (New York, 1951).Google Scholar