Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

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.