Symmetry analysis of the two-dimensional diffusion equation with a source term

A symmetry analysis is performed on a (2 + 1)-dimensional linear diffusion equation with a nonlinear source term involving the dependent variable and its spatial derivatives. In the first part of the paper, we use the classical method to classify source terms where the original equation admits a nontrivial symmetry. In the second part of the paper, we use the nonclassical method and show that we simply recover the classical symmetries. © 2006 Elsevier Inc. All rights reserved