Mapping method of group classification

We revisit the entire framework of group classification differential equations. After introducing notion weakly similar classes equations, we develop mapping method for such classes, which generalizes all versions this that have been presented in literature. The is applied to various Kolmogorov equations and Fokker-Planck case space dimension one. equivalence groupoids groups these are computed. problems with respect corresponding reduced finding inequivalent solutions heat potentials admitting Lie-symmetry extensions. This reduction allows us exhaustively solve time-independent coefficients.