Z. Naturforsch. **68a,** 391 – 397
(2013)

doi:10.5560/ZNA.2013-0007

Approximate Functional Variable Separation for the Quasi-Linear Diffusion Equations with Weak Source

Fei-Yu
Ji

College of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China

Received October 16, 2012 / revised January 9, 2013 / published online February 20, 2013

As an extension to the functional variable separation approach, the approximate functional variable separation approach is proposed, and it is applied to study the quasi-linear diffusion equations with weak source. A complete classification of these perturbed equations which admit approximate functional separable solutions is obtained. As a result, the corresponding approximate functional separable solutions to the resulting perturbed equations are derived via examples.

*Key words:* Quasi-Linear Diffusion Equation; Approximate Functional Separable Solution; Approximate Generalized Conditional Symmetry.

*PACS numbers:* 02.30.Jr; 02.20.Sv; 02.30.Ik