Analytical solutions for a nonlinear diffusion equation with convection and reaction

2014 ◽  
Vol 416 ◽  
pp. 439-451 ◽  
Author(s):  
C. Valenzuela ◽  
L.A. del Pino ◽  
S. Curilef
Keyword(s):  
Diffusion Equation ◽  
Analytical Solutions ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation

scholarly journals Equations for nonlinear diffusion

2010 ◽  
Vol 51 ◽  
Author(s):  
Arvydas Juozapas Janavičius
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Analytical Solutions ◽  
Nonlinear Diffusion ◽  
Diffusion Time ◽  
Nonlinear Diffusion Equation ◽  
Square Root ◽  
Brownian Movement ◽  
Finite Velocity

The diffusion is the result of Brownian movement and occurs with a finite velocity. We presented the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. Analytical solutions, showing that the maximum displacements of diffusing particles are proportional to the square root of diffusion time like for Brownian movement, was obtained. For small concentrations of impurities, nonlinear diffusion equation transforms to linear.

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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