Email this article Methods of group classification for relaxing gasdynamics
- Authors: Khabirov S.V.1
-
Affiliations:
- Mavlyutov Institute of Mechanics UFRC RAS
- Issue: Vol 88, No 6 (2024)
- Pages: 944-958
- Section: Articles
- URL: https://ruspoj.com/0032-8235/article/view/678444
- DOI: https://doi.org/10.31857/S0032823524060092
- EDN: https://elibrary.ru/IGMBOH
- ID: 678444
Cite item
Open Access
Access granted
Abstract
Group classification is the basic problem of the group analysis of differential equations with an arbitrary element. For the equations of the ideal gas dynamics with a state equation invariable on time the problem was solved by enumerating simplifications of the determining relations using equivalence transformations. For a state equation depending on time the exhaustive search is vast and it can be used optimal systems of subalgebras for the subalgebra extending the kernel of admitted algebras. Combination of the both methods solves the problem of the group classification for the relaxing gas dynamics.
Full Text
About the authors
S. V. Khabirov
Mavlyutov Institute of Mechanics UFRC RAS
Author for correspondence.
Email: habirov@anrb.ru
Russian Federation, Ufa
References
- Ovsyannikov L.V. The “podmodeli” program. Gas dynamics // JAMM, 1994, vol. 58, iss. 4, pp. 601–627.
- Ovsyannikov L.V. Some results of the implementation of the “podmodeli” program for the gas dynamics equations // JAMM, 1999, vol. 58, iss. 4, pp. 349–358
- Borisov A.V., Khabirov S.V. Equivalence transformations for gas dynamics equations // Multiphase Syst., 2024, vol. 19, no. 2, pp. 44–48.
- Ovsyannikov L.V. Group Analysis of Differential Equations. Moscow: Nauka. 1978. 399 p. (in Russian)
- Chirkunov Yu.A., Khabirov S.V. Elements of Symmetry Analysis of Differential Equations of Continuum Mechanics. Novosibirsk: NSTU, 2012. 659 p.
- Mukminov T.M., Khabirov S.V. Graph of nested subalgebras of the 11-dimensional symmetry algebra of a continuous medium // SEMI, 2019, vol. 16, pp. 121–143.
- Khabirov S.V. Classification of differentially invariant submodels // Sib. Math. J., 2004, vol. 45, no. 3, pp. 682–701.
- Mukminov T.M., Khabirov S.V. Simple waves of conical motions // Ufa J. of Math., 2022, vol. 14, no. 2, pp. 82–93.
- Vaneeva O.O., Bihlo A., Popovich R.O. Equivalence groupoid and group classification of a class of nonlinear wave and elliptic equations // arXiv:2002.08939v1 [math-ph] 20 Feb 2020. 38 p.
- Malkin A.Ya., Isaev A.I. Rheology: Concepts, Methods, Applications. St. Petersburg: Professiya Pub., 2010. 557 p.
- Vladimirov V.A. Modelling system for relaxing media. Symmetry, restrictions and attractive features of invariant solution // Proc. of Inst. of Mathematics of NASU, 2000, vol. 30, Pt. 1, pp. 231–238.
- Khabirov S.V. Group classification of ideal gas-dynamic relaxing media by equivalence transformations // Sib. Math. J., 2023, vol. 64, no. 4, pp. 936–954.
- Khabirov S.V. On group classification of ideal gas-dynamic relaxing media // Proc. of the Krasovskii Inst. of Mathematics and Mechanics of the UB RAS, 2023, vol. 29, no. 2, pp. 260–270.
- Khabirov S.V. On group classification of relaxing gas dynamics by the method of optimal system of subalgebras // Sib. Math. J., 2025, vol. 66, no. 1, pp. 106–128.
Supplementary files
