Research of equations of a viscous inhomogeneous fluid in a Hele–Shaw cell by group analysis method

The main group of transformations allowed by the system of differential equations for the flow of a viscous inhomogeneous fluid in a Hele–Shaw cell is constructed in this paper. A classifying equation for the viscosity function is obtained. A basis of operators that preserve the form of the original equations is constructed. The basis of the space of solutions of defining equations is described. Invariants of operators are found and invariant solutions of the equations are obtained.