Invariant submodel of rank 2 on subalgebra of translations linear combinations for a hydrodynamic type model

The equations of hydrodynamic type with the equation of state in the form of pressure, represented as a sum of density and entropy functions, are considered in the article. For the invariant submodel of a 2-dimensional subalgebra in the form of a linear combination of translations chosen from the previously constructed optimal system of non-similar subalgebras, we find the integrals of the system, determine the type of the system, reduce the system to the symmetric form and the characteristic form, find exact solutions, define equivalence transformations for the linearized system, the group classification problem is solved, an optimal system of non-similar subalgebras is constructed, and the application of integral transformations is shown.