scholarly journals A similarity solution to a nonlinear diffusion equation of the singular type: a uniformly valid solution by perturbations

1979 ◽  
Vol 37 (1) ◽  
pp. 11-21 ◽  
Author(s):  
D. K. Babu ◽  
M. Th. van Genuchten
Keyword(s):  
Diffusion Equation ◽  
Similarity Solution ◽  
Nonlinear Diffusion ◽  
Type A ◽  
Nonlinear Diffusion Equation ◽  
Valid Solution

NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW

2021 ◽  
Vol 10 (5) ◽  
pp. 2611-2624
Author(s):  
O.K. Narain ◽  
F.M. Mahomed
Keyword(s):  
Diffusion Equation ◽  
Conservation Law ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
The Other ◽  
Linear Case ◽  
Exact Equation ◽  
Convection Term ◽  
Potential Symmetries ◽  
Perturbed Equation

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

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