  In this investigation, symmetry properties of the nonlinear heat conductivity
equations of general form $u_t = [E(x, u)u_x]_x + H(x, u)$ 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.
