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DOI 10.21662
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Siraeva D.T. Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels. Multiphase Systems. 13 (2018) 3. 59–63.
2018. Vol. 13. Issue 3, Pp. 59–63
URL: http://mfs.uimech.org/mfs2018.3.009
DOI: 10.21662/mfs2018.3.009
Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels
Siraeva D.T.
Mavlutov Institute of Mechanics, UFRC RAS, Ufa

Abstract

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

Keywords

subalgebra,
invariant,
partially invariant submodel,
hydrodynamics

Article outline

Purpose: The purpose is construction of partially invariant submodels of rank 3 defect 1 and proof of their reduction to invariant submodels.

Methodology: The methods of the theory of differential equations, mathematical physics, and group analysis are used.

Findings: Two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras 2.38, 2.39 of the twelve-dimensional Lie algebra for equations of hydrodynamic type with the equation of state in the form of pressure separated into the sum of density and entropy functions. We proved the reduction of the constructed partially invariant submodels to invariant submodels of rank 3 of eleven-dimensional and twelve-dimensional Lie algebras, respectively.

References

  1. Овсянников Л.В. Программа ПОДМОДЕЛИ. Газовая динамика // Прикладная математика и механика. Москва: РАН. 1994. Т. 58, вып. 4. C. 30–55.
  2. Хабиров С.В. Неизоморфные алгебры Ли, допускаемые моделями газовой динамики // Уфимский математический журнал. 2011. Т. 3, вып. 2. С. 87–90.
    (http://mi.mathnet.ru/rus/ufa/v3/i2/p87)
  3. Khabirov S.V. Optimal system for sum of two ideals admitted by hydrodynamic type equations // Ufa Mathematical Journal. 2014. Vol. 6, i. 2. Pp. 97–101.
    (10.13108/2014-6-2-97).
  4. Siraeva D.T. Optimal system of non-similar subalgebras of sum of two ideals // Ufa Mathematical Journal. 2014. Vol. 6, i. 1. Pp. 90—103.
    (10.13108/2014-6-1-90).
  5. Хабиров С.В. Аналитические методы в газовой динамике. Уфа. Гилем. 2003. 192 с.
  6. Чиркунов Ю.А., Хабиров С.В. Элементы симметрийного анализа дифференциальных уравнений механики сплошной среды: монография. Новосибирск: Издательство НГТУ, 2012. 659 с.