Article
Ufa Mathematical Journal
Volume 4, Number 4, pp. 143-150
Extension of the conic flows
Khabirov S.V.
Download PDF
Article on MathNetAbstact
All partial invariant solutions of gas dynamic equations, that are constructed on the conic subalgebra admitted by the model are found. The conic subalgebra consists of operators of rotation, translation by time and expansion. A submodel comprises a system of ordinary differential equations. Solutions form a series of submodels. In the basis of these submodels lies conic submodel with respect to the invariant variable depending on independent variables and constants of the submodels depending on an invariant function. To determine this dependence, various additional overdetermined equations are obtained. Moreover, two submodels, expanding the conic submodel, are derived from the system of partial differential equations. All formulas mapping the solutions to physical space are defined for these two submodels.