Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative

2013 ◽  
Vol 261 ◽  
pp. 85-91 ◽  
Author(s):  
Łukasz Płociniczak ◽  
Hanna Okrasińska
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Self Similar ◽  
Time Fractional Derivative ◽  
Similar Solutions

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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