Geodesic
An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 61-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

The present study is devoted to 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 co-ordinate net. An optimal system of one-dimensional subalgebras constructing algorithm for the Lie algebra is proposed. The optimal system (total 187 elements) is shown consist of a 3-parametrical element, twelve 2-parametrical elements, sixty six 1-parametrical elements and one hundred and eight individual elements. 
@article{ISU_2011_11_2_a9,
     author = {V. A. Kovalev and Yu. N. Radayev},
     title = {An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {61--77},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a9/}
}
TY  - JOUR
AU  - V. A. Kovalev
AU  - Yu. N. Radayev
TI  - An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2011
SP  - 61
EP  - 77
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a9/
LA  - ru
ID  - ISU_2011_11_2_a9
ER  - 
%0 Journal Article
%A V. A. Kovalev
%A Yu. N. Radayev
%T An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2011
%P 61-77
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a9/
%G ru
%F ISU_2011_11_2_a9
V. A. Kovalev; Yu. N. Radayev. An optimal system constructing algorithm for symmetry algebra of three-dimensional equations of the perfect plasticity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 61-77. http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a9/

[1] Ivlev D. D., “O sootnosheniyakh, opredelyayuschikh plasticheskoe techenie pri uslovii plastichnosti Treska, i ego obobscheniyakh”, Dokl. AN SSSR, 124:3 (1959), 546–549 | MR | Zbl

[2] Radaev Yu. N., “O kanonicheskikh preobrazovaniyakh Puankare i invariantakh uravnenii plasticheskogo ravnovesiya”, Izv. AN SSSR. Mekhanika tverdogo tela, 1990, no. 1, 86–94

[3] Radaev Yu. N., Prostranstvennaya zadacha matematicheskoi teorii plastichnosti, 2-e izd., pererab. i dop., Izd-vo Samar. gos. un-ta, Samara, 2006, 340 pp.

[4] Radaev Yu. N., Gudkov V. A., “Ob odnoi estestvennoi konechnomernoi podalgebre algebry simmetrii trekhmernykh uravnenii matematicheskoi teorii plastichnosti”, Vestn. Samar. gos. un-ta. Estestvennonauchnaya ser., 2005, no. 5(39), 52–70 | MR

[5] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978, 400 pp. | MR | Zbl

[6] Olver P. J., Application of Lie Groups to Differential Equations, Springer, N.Y., 1986, v russkom perevode sm. [7] | MR | Zbl

[7] Olver P., Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989, 639 pp. | MR | Zbl

[8] Olver P. J., Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge–N.Y.–Melbourne, 1995, 526 pp. | MR | Zbl

[9] Kovalev V. A., Radaev Yu. N., Elementy teorii polya: variatsionnye simmetrii i geometricheskie invarianty, Fizmatlit, M., 2009, 156 pp.

[10] Kovalev V. A., Radaev Yu. N., Volnovye zadachi teorii polya i termomekhanika, Izd-vo Sarat. un-ta, Saratov, 2010, 328 pp.