Z. Naturforsch. 68a, 621 – 628
Classification and Approximate Functional Separable Solutions to the Generalized Diffusion Equations with Perturbation
1 College of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China
2 Department of Mathematics, Northwest University, Xi'an 710069, China
Received May 17, 2013 / published online October 2, 2013
In this paper, the generalized diffusion equation with perturbation ut = A(u, ux)uxx + ϵB(u, ux) is studied in terms of the approximate functional variable separation approach. A complete classification of these perturbed equations which admit approximate functional separable solutions is presented. Some approximate solutions to the resulting perturbed equations are obtained by examples.
Key words: Diffusion Equation; Approximate Functional Separable Solutions; Approximate Functional Variable Separation Approach.
PACS numbers: 02.30.Jr; 02.20.Sv; 02.30.Ik