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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2011, Issue 1(22), Pages 196–220
DOI: https://doi.org/10.14498/vsgtu860 (Mi vsgtu860) 		 
Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mechanics

An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity

V. A. Kovaleva, Yu. N. Radaevb

a Dept. of Applied Mathematics, Moscow City Government University of Management Moscow
b Lab. of Modeling in Solid Mechanics, A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.14498/vsgtu860
Abstract: The present paper is devoted to a study of a natural $12$-dimensional symmetry algebra of the three-dimensional hyperbolic differential equations of the perfect plasticity, obtained by D. D. Ivlev in 1959 and formulated in isostatic coordinates. An optimal system of one-dimensional subalgebras constructing algorithm for the Lie algebra is proposed. The optimal system (total $187$ elements) is shown consisting of of a 3-parametrical element, twelve 2-parametrical elements, sixty six 1-parametrical elements and one hundred and eight individual elements.
Keywords: theory of plasticity, isostatic coordinate, symmetry group, symmetry algebra, subalgebra, optimal system, algorithm.
Original article submitted 20/XII/2010
revision submitted – 18/II/2011
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74C05
Language: Russian
Citation: V. A. Kovalev, Yu. N. Radaev, “An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 196–220
Citation in format AMSBIB
\Bibitem{KovRad11}
\by V.~A.~Kovalev, Yu.~N.~Radaev
\paper An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 196--220
\mathnet{http://mi.mathnet.ru/vsgtu860}
\crossref{https://doi.org/10.14498/vsgtu860}
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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