Separation of variables of a generalized porous medium equation with nonlinear source

This paper considers a general form of the porous medium equation with nonlinear source term: ut = (D(u)unx )x + F(u), n = 1. The functional separation of variables of this equation is studied by using the generalized conditional symmetry approach. We obtain a complete list of canonical forms for such equations which admit the functional separable solutions. As a consequence, some exact solutions to the resulting equations are constructed, and their behavior are also investigated.  2002 Elsevier Science (USA). All rights reserved.