Selçuk Journal
of
Applied Mathematics
SummerAutumn, 2002
Volume 3
Number 2
Research Center
of
Applied Mathematics

SJAM
SummerAutumn 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 :
habirov@anrb.ru ;
Received:
March 26, 2001^{
} 
Summary
For
an arbitrary state
equation the
gasdynamics
equations admit
the 11dimensional
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
6dimensional 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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