The nonlinear diffusion and thermal conductivity equation: group classification and exact solutions (Q1417158)

For the nonlinear equation \(u_t=(u^\alpha u_x)_x+F(u)\), \(0\not =\alpha\in \mathbb R,\) describing processes of nonlinear diffusion and thermal conductivity the authors present group classification with respect to contact transformations. The resulting Lie algebra allows to determine some exact solutions.