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.

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.

Asymptotic solutions of the Erdogan-Chatwin equation

1978 ◽  
Vol 88 (2) ◽  
pp. 323-337 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Approximate Solution ◽  
Diffusion Equation ◽  
Pipe Flow ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Asymptotic Solutions ◽  
Initial Value ◽  
Concentration Jump ◽  
Buoyancy Correction

Erdogan & Chatwin (1967) derived a nonlinear diffusion equation\[ \partial_tc = \partial_z([D_0+(\partial_zc)^2D_2]\partial_zc) \]which models the effect of buoyancy upon the longitudinal dispersion of a solute in pipe flow. The same equation arises more widely as a limiting form in which only the first buoyancy correction is retained. In this paper long-term asymptotic solutions are obtained both for the smearing-out of a concentration jump and for the approach to normality of a finite discharge. A variant of the method provides an approximate solution to the initial-value problem, and a comparison is made with Prych's (1970) experimental results.

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