scholarly journals On the group classification of variable-coefficient nonlinear diffusion–convection equations

2006 ◽  
Vol 197 (2) ◽  
pp. 322-344 ◽  
Author(s):  
N.M. Ivanova ◽  
C. Sophocleous
Keyword(s):  
Nonlinear Diffusion ◽  
Variable Coefficient ◽  
Group Classification ◽  
Diffusion Convection

scholarly journals New results on group classification of nonlinear diffusion–convection equations

2004 ◽  
Vol 37 (30) ◽  
pp. 7547-7565 ◽  
Author(s):  
Roman O Popovych ◽  
Nataliya M Ivanova
Keyword(s):  
Nonlinear Diffusion ◽  
Group Classification ◽  
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.

Group Classification of Variable Coefficient $K\MakeLowercase{(m,n)}$ Equations

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Classification

scholarly journals Enhanced group classification of nonlinear diffusion–reaction equations with gradient-dependent diffusivity

2020 ◽  
Vol 484 (1) ◽  
pp. 123739 ◽  
Author(s):  
Stanislav Opanasenko ◽  
Vyacheslav Boyko ◽  
Roman O. Popovych
Keyword(s):  
Nonlinear Diffusion ◽  
Group Classification ◽  
Diffusion Reaction ◽  
Reaction Equations

scholarly journals Group analysis of variable coefficient diffusion-convection equations. I. Enhanced group classification

2010 ◽  
Vol 31 (2) ◽  
pp. 100-122 ◽  
Author(s):  
N. M. Ivanova ◽  
R. O. Popovych ◽  
C. Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Analysis ◽  
Group Classification ◽  
Diffusion Convection

scholarly journals Group Classification of Variable Coefficient K(m,n) Equations

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Classification
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