scholarly journals On the Multiplicity of Equilibrium Solutions to a Nonlinear Diffusion Equation on a Manifold Arising in Climatology

1997 ◽  
Vol 216 (2) ◽  
pp. 593-613 ◽  
Author(s):  
J.I. Dı́az ◽  
J. Hernández ◽  
L. Tello
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Equilibrium 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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