Group classification of ideal gas-dynamic relaxing media by the method of an optimal system of subalgebras

Group classification is the basic problem in the group analysis of differential equations with an arbitrary element. For the equations of ideal gas dynamics with a stationary state equation the problem is solved with a brute-force search of simplifications of the defining relations by equivalence transformations. For time-dependent relaxation state equations, the brute-force search is huge, and we have to use an optimal system of subalgebras of a subalgebra extending the core of admitted algebras. Some combination of both methods leads to a solution of the problem of group classification of gas-dynamic relaxation.