Exact solutions of the diffusion-convection equation in cylindrical geometry

2005 ◽  
Vol 12 (10) ◽  
pp. 102511 ◽  
Author(s):  
S. P. Eury ◽  
E. Harauchamps ◽  
X. L. Zou ◽  
G. Giruzzi
Keyword(s):  
Exact Solutions ◽  
Cylindrical Geometry ◽  
Convection Equation ◽  
Diffusion Convection

Exact solution of the diffusion-convection equation in cylindrical geometry

AIChE Journal ◽  
2011 ◽  
Vol 58 (4) ◽  
pp. 1299-1302 ◽  
Author(s):  
Oleksandr Ivanchenko ◽  
Nikhil Sindhwani ◽  
Andreas A. Linninger
Keyword(s):  
Exact Solution ◽  
Cylindrical Geometry ◽  
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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