On The Adjoint of a Nonlinear Diffusion-Convection Equation to Describe Flow in Porous Media

2005 ◽  
Author(s):  
Ali Vakili ◽  
Jan-Dirk Jansen ◽  
C.P.J.W. van Kruijsdijk ◽  
Talal Ebraheem Esmaiel
Keyword(s):  
Porous Media ◽  
Nonlinear Diffusion ◽  
Flow In Porous Media ◽  
Convection Equation ◽  
Diffusion Convection

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

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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