Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption

This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D(u)ux )x + Q(x, u)ux + P(x,u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x. © 2007 Elsevier Inc. All rights reserved.