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

Abstract

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.