Group of symmetries for the dynamics system of equations of rarefied two-phase medium

The symmetries of the system of equations of a two-phase medium are found, where the first phase is gas and the second one is solid particles. The second phase is considered rarefied, it is expressed in the absence of pressure in the equations of motion of the second phase. The medium is assumed to be nonisothermal. Using the methods of group analysis, the Lie algebras of symmetries of the model under study are found in the one-dimensional and three-dimensional cases. The paper describes in detail the process of searching for symmetries in the case of equations of state for a perfect gas. Some partially invariant solutions are found for the one-domensional system.