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Optimal Systems of Symmetry Subalgebras for Big Models of Gasdynamics
Abstract
The gasdynamics equations admit 11 dimensional Lie algebra
of transformations for the arbitrary 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 subalgebras are calculated. This will be helpful in
the calculation of the full optimal systems.
Mathematics Subject Classification (1991): 35Q35
Keywords: symmetry, other equations arising in fluid dynamics, gasdynamics,
state equation, Lie algebra of transformations, optimal systems of subalgebras,
Lie, algebra, transformations, extensions
Quaestiones Mathematicae 24(2) 2001, 133-146
of transformations for the arbitrary 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 subalgebras are calculated. This will be helpful in
the calculation of the full optimal systems.
Mathematics Subject Classification (1991): 35Q35
Keywords: symmetry, other equations arising in fluid dynamics, gasdynamics,
state equation, Lie algebra of transformations, optimal systems of subalgebras,
Lie, algebra, transformations, extensions
Quaestiones Mathematicae 24(2) 2001, 133-146
