Group classification and exact solutions of equations of the type of nonlinear thermal conductivity

Abstract:
For the class of equations of the type of nonlinear thermal conductivity $w_t=H(w_{xx})$ the proof of the results of the group classification of I.Sh. Akhatov, R.K. Gazizov, N.H. Ibragimov (1989) is precised. The finite group transformations and formulas of generation of solutions are presented. The one-dimensional subalgebras of invariant algebras and reductions to ordinary differential equations are described, and some classes of exact solutions are obtained.