Methods of group classification for relaxing gasdynamics

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

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.

Texto integral

Acesso é fechado

Sobre autores

S. Khabirov

Mavlyutov Institute of Mechanics UFRC RAS

Autor responsável pela correspondência
Email: habirov@anrb.ru
Rússia, Ufa

Bibliografia

  1. Ovsyannikov L.V. The “podmodeli” program. Gas dynamics // JAMM, 1994, vol. 58, iss. 4, pp. 601–627.
  2. 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
  3. Borisov A.V., Khabirov S.V. Equivalence transformations for gas dynamics equations // Multiphase Syst., 2024, vol. 19, no. 2, pp. 44–48.
  4. Ovsyannikov L.V. Group Analysis of Differential Equations. Moscow: Nauka. 1978. 399 p. (in Russian)
  5. Chirkunov Yu.A., Khabirov S.V. Elements of Symmetry Analysis of Differential Equations of Continuum Mechanics. Novosibirsk: NSTU, 2012. 659 p.
  6. 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.
  7. Khabirov S.V. Classification of differentially invariant submodels // Sib. Math. J., 2004, vol. 45, no. 3, pp. 682–701.
  8. Mukminov T.M., Khabirov S.V. Simple waves of conical motions // Ufa J. of Math., 2022, vol. 14, no. 2, pp. 82–93.
  9. 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.
  10. Malkin A.Ya., Isaev A.I. Rheology: Concepts, Methods, Applications. St. Petersburg: Professiya Pub., 2010. 557 p.
  11. 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.
  12. 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.
  13. 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.
  14. 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.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar
2. Appendix. Optimal system of subalgebras in the case γs=0, N=0
Baixar (270KB)
Metadados

Declaração de direitos autorais © Russian Academy of Sciences, 2024