Group Classification of Ideal Gas-Dynamic Relaxing Media by Equivalence Transformations

We solve the main problems of group analysis for differential equations of ideal gas dynamics on assuming that the state equation for thermodynamic parameters is independent of time. Using group analysis, we study a relaxing medium that changes with time, for example, as a result of rheology or due to energy averaging of processes in a multiphase medium. Equivalence transformations change the state equation rather than the motion equation. The computations of equivalence transformations define some preliminary group classification, i.e., the classes of state equations such that the group of equivalence transformations changes. We show that projective transformations apply to more general than stationary state equations. Also, we propose some new constructive method for group classification by calculating equivalence transformations with additional conditions on the state equations that appear while analyzing the invariance conditions.