Selšuk Journal of Applied Mathematics

 Selšuk Journal of
  Applied Mathematics

  Summer-Autumn, 2002
  Volume  3
  Number 2

Research Center of 
  Applied Mathematics

 SJAM Summer-Autumn 2002, Volume 3 - Number 2

Optimal systems of symmetry subalgebras for big models of gasdynamics

Salavat Khabirov

Institute of Mechanics, UB RAS , Marx street 12, 450000 Ufa, Russia
   email : ;

   Received: March 26, 2001

For an arbitrary state equation the gasdynamics equations admit the 11-dimensional Lie algebra of transformations. But there are 13 special state equations for which the corresponding Lie algebra of transformations may be expanded. In this event we call the gasdynamics equations the big models. Some of the Lie algebras under consideration are similar to one another and the algebra structure may be different under further specialization of the state equation. It was noted that only two specializations of the state equation need to be added into consideration. In the paper we make a review of extensions for which the optimal systems of subalgebras may be found and calculate these optimal systems. Each of the extensions is presented as the semidirect sum of the Abelian 6-dimensional ideal and a subalgebra. The normalized optimal systems of these subalgebras are calculated.


Key words
gasdynamics, state equation, Lie algebra of transformations, optimal systems of subalgebras.

2000 Mathematics Subject Classification : 37K30, 76N15

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