OPTIMAL SYSTEMS OF SYMMETRY SUBALGEBRAS FOR BIG MODELS OF GASDYNAMICS

Abstract

The gasdynamics equations admit 11 dimensional Lie algebra of transformations for the abitrary state equations. For special state equations the algebra may be expanded. There are 13 special state equations for which the gasdynamics equations are named big models. Some of the algebras are similar. The algebra structure may be different under further specialization of the state equations. It was noted in the calculation process of the expansion of optimal systems that only 2 such specializations need to be added. We make a review of extensions for which the optimal systems of subalgebras are calculated. Each of the extensions are presented as semidirect sums of Abelian 6 dimensional ideal and subalgebra. The normalized optimal systems of these sub-algebras are calculated. This will be helpful in the calculation of the full optimal systems.