Z. Naturforsch. **68a,** 621 – 628
(2013)

doi:10.5560/ZNA.2013-0058

Classification and Approximate Functional Separable Solutions to the Generalized Diffusion Equations with Perturbation

Fei-Yu
Ji^{1} and
Shun-Li
Zhang^{2}

^{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 *u*_{t} = *A*(*u*, *u*_{x})*u*_{xx} + *ϵB*(*u*, *u*_{x}) 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