ISSN 2658–5782
DOI 10.21662
DOI 10.21662
Electronic Scientific Journal
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.
subalgebra,
invariant,
partially invariant submodel,
hydrodynamics
Purpose: The purpose is construction of partially invariant submodels of rank 3 defect 1 and proof of their reduction to invariant submodels.
Methodology: The methods of the theory of differential equations, mathematical physics, and group analysis are used.
Findings: Two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras 2.38, 2.39 of the twelve-dimensional Lie algebra for equations of hydrodynamic type with the equation of state in the form of pressure separated into the sum of density and entropy functions. We proved the reduction of the constructed partially invariant submodels to invariant submodels of rank 3 of eleven-dimensional and twelve-dimensional Lie algebras, respectively.
