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Symmetries and conservation laws of 2-dimensional ideal plasticity

Published online by Cambridge University Press:  20 January 2009

S. I. Senashov
Affiliation:
Department of MathematicsKrasnojarsky University660062 Krasnojarsk, U.S.S.R.
A. M. Vinogradov
Affiliation:
Department of MathematicsMoscow University117234 Moscow, U.S.S.R.
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Symmetry theory is of fundamental importance in studying systems of partial differential equations. At present algebras of classical infinitesimal symmetry transformations are known for many equations of continuum mechanics [1, 2, 4]. Methods foi finding these algebras go back to S. Lie's works written about 100 years ago. Ir particular, knowledge of symmetry algebras makes it possible to construct effectively wide classes of exact solutions for equations under consideration and via Noether's theorem to find conservation laws for Euler–Lagrange equations. The natural development of Lie's theory is the theory of “higher” symmetries and conservation laws [5].

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Annin, B. D., Bytev, V. O. and Senashov, S. I., Group Properties of Elasticity and Plasticity Equations (“Nauka”, Novosibirsk, 1985, in Russian).Google Scholar
2.Ibragimov, N. H., Group Transformations in the Mathematical Physics (“Nauka”, Moscow, 1983, English translations: Reidel, 1985).Google Scholar
3.Krasil'Shchik, I. S., Lychagin, V. V. and Vinogradov, A. M., Geometry of Jet Spaces and Nonlinear Partial Differential Equations (Gordon and Breach, New York, 1986).Google Scholar
4.Ovsiannikov, L. V., Group Analysis of Differential Equations (“Nauka”, Moscow, 1978, English translation: Academic Press, 1982).Google Scholar
5.Vinogradov, A. M., Local symmetries and conservation laws, Acta Appl Math. 2 (1984), 2178.CrossRefGoogle Scholar