Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

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.

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Approximate Derivative-Dependent Functional Variable Separation for the Generalized Diffusion Equations with Perturbation

Communications in Theoretical Physics ◽

10.1088/0253-6102/58/2/01 ◽

2012 ◽

Vol 58 (2) ◽

pp. 175-181 ◽

Cited By ~ 2

Author(s):

Shun-Li Zhang ◽

Fei-Yu Ji ◽

Chang-Zheng Qu

Keyword(s):

Diffusion Equations ◽

Variable Separation ◽

Functional Variable ◽

Approximate Derivative

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Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion–convection equations with weak source

Modern Physics Letters B ◽

10.1142/s0217984918500938 ◽

2018 ◽

Vol 32 (07) ◽

pp. 1850093

Author(s):

Ya-Rong Xia ◽

Shun-Li Zhang ◽

Xiang-Peng Xin

Keyword(s):

Nonlinear Diffusion ◽

Invariant Subspaces ◽

Complete Classification ◽

Variable Separation ◽

Weak Source ◽

Convection Equation ◽

Functional Variable ◽

Diffusion Convection

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion–convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

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

Zeitschrift für Naturforschung A ◽

10.5560/zna.2013-0058 ◽

2013 ◽

Vol 68 (10-11) ◽

pp. 621-628

Author(s):

Fei-Yu Ji ◽

Shun-Li Zhang

Keyword(s):

Diffusion Equation ◽

Approximate Solutions ◽

Complete Classification ◽

Diffusion Equations ◽

Variable Separation ◽

Functional Variable ◽

Variable Separation Approach

In this paper, the generalized diffusion equation with perturbation ut = A(u;ux)uII+eB(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.

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