Symmetry classifications and reductions of some classes of (2+1)-nonlinear heat equation

The (2 + 1)-nonlinear heat equation ut − f (u)(uxx + uyy ) = 0 is considered. A symmetry classification of the equation using Lie group method is presented and reduction to the first- or second-order ordinary differential equations is provided. © 2007 Elsevier Inc. All rights reserved