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Zeitschrift für Naturforschung A Contents Vol. 68a (2013)

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 Ji¹ and Shun-Li Zhang²

¹College of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China

²Department of Mathematics, Northwest University, Xi'an 710069, China

Received May 17, 2013 / published online October 2, 2013

Reprint requests to: F.-Y. J.; E-mail: feiyuji@xauat.edu.cn

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

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