Symmetry classification for the nonlinear heat conductivity equation

In this investigation, symmetry properties of the nonlinear heat conductivity equations of general form ut = [E(x, u)ux]x + H(x, u) are studied. The point symmetry analysis of these equations is considered as well as an equivalence classification which admits an extension by one dimension of the principal Lie algebra of them. The invariant solutions of equivalence transformations and classification of the nonlinear heat conductivity equations among with additional operators are also given.