Group Analysis of Gas Dynamics Equations for a Dissociating Gas in Two Spatial Dimensions in Eulerian and Lagrangian Coordinates

comprehensive group analysis of two-dimensional flows of a chemically reacting ideal gas with a two-component mixture is carried out. The study covers both unsteady and stationary regimes, considered in Eulerian and Lagrangian coordinates. By exploiting equivalent transformations and use of optimal systems of subalgebras for classification procedure, the governing equations are classified into four distinct classes depending on the reaction rate function. The Lagrangian formulation of solutions stationary in Eulerian coordinates is given: the group classification of such equations is also presented. In addition, the case of a mixture of two non-interacting gases is analyzed as a natural limiting model. A class of partially invariant solutions is obtained through compatibility analysis and reduction to involutive form, followed by a generalization that reduces the governing equations to systems with two independent variables while retaining essential two-dimensional features. These generalized solutions admit self-similar forms and extend the classical similarity solutions of the strong explosion problem to incorporate transverse velocity components, thereby revealing the role of two-dimensionality. The results establish a coherent framework for the classification and construction of invariant and partially invariant solutions for reacting and non-reacting gas mixtures, with potential applications to twodimensional gas dynamics, magnetohydrodynamics, and invariant numerical schemes.