scholarly journals A supnorm estimate for one-dimensional porous medium equations with advection

2017 ◽  
Author(s):  
Juliana Ziebell ◽  
Lucinéia Fabris ◽  
Janaina Zingano ◽  
Linéia Schütz
Keyword(s):  
Porous Medium ◽  
One Dimensional ◽  
Porous Medium Equations

scholarly journals Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection

2019 ◽  
Vol 22 (03) ◽  
pp. 1950015
Author(s):  
Filomena Feo ◽  
Yanghong Huang ◽  
Bruno Volzone
Keyword(s):  
Porous Medium ◽  
Exponential Convergence ◽  
Porous Medium Equation ◽  
Entropy Method ◽  
Nonlocal Diffusion ◽  
One Dimensional ◽  
Medium Equation ◽  
Long Time ◽  
Porous Medium Equations ◽  
Long Time Asymptotics

In this paper, the long-time asymptotic behaviors of one-dimensional porous medium equations with a fractional pressure and absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted to derive the exponential convergence of relative entropy of solutions in similarity variables.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

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