Abstract:
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.
This publication is cited in the following 4 articles:
Dilara Siraeva, “Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation”, International Journal of Non-Linear Mechanics, 2024, 104904
Renata Nikonorova, Dilara Siraeva, Yulia Yulmukhametova, “New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations”, Mathematics, 10:1 (2022), 123
D Siraeva, “Invariant submodel of rank 1 and two families of exact solutions of gas dynamics equations with an equation of state of the special form”, J. Phys.: Conf. Ser., 2099:1 (2021), 012017
D T Siraeva, “Two invariant submodels of rank 1 of the hydrodynamic type equations and exact solutions”, J. Phys.: Conf. Ser., 1666:1 (2020), 012049
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