Solutions for a fractional nonlinear diffusion equation: Spatial time dependent diffusion coefficient and external forces

2004 ◽  
Vol 45 (9) ◽  
pp. 3444-3452 ◽  
Author(s):  
E. K. Lenzi ◽  
R. S. Mendes ◽  
Kwok Sau Fa ◽  
L. R. da Silva ◽  
L. S. Lucena
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Time Dependent ◽  
External Forces

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.

scholarly journals Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/u

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 804 ◽  
Author(s):  
Philip Broadbridge ◽  
Joanna M. Goard
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Meromorphic Functions ◽  
Nonlinear Diffusion Equation ◽  
Direct Application ◽  
Time Dependent ◽  
Flux Boundary Conditions ◽  
General Complex ◽  
Laser Heated ◽  
Special Time

An explicit mapping is given from the space of general complex meromorphic functions to a space of special time-dependent solutions of the 1 + 2-dimensional nonlinear diffusion equation with diffusivity depending on concentration as D = 1 / u. These solutions have constant-flux boundary conditions. Some simple examples are constructed, including that of a line source enclosed by a cylindrical barrier. This has direct application to electron diffusion in a laser-heated plasma.

scholarly journals The nonlinear diffusion equation of the ideal barotropic gas through a porous medium

2017 ◽  
Vol 15 (1) ◽  
pp. 895-906
Author(s):  
Huashui Zhan
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Well Posedness ◽  
Initial Value ◽  
Barotropic Gas ◽  
The Ideal

Abstract The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of the solutions may be obtained without any boundary condition.

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