Asymptotic Behaviour and Propagation Properties of the One-Dimensional Flow of Gas in a Porous Medium

1983 ◽  
Vol 277 (2) ◽  
pp. 507 ◽  
Author(s):  
Juan Luis Vazquez
Keyword(s):  
Porous Medium ◽  
Asymptotic Behaviour ◽  
One Dimensional ◽  
Dimensional Flow ◽  
The One ◽  
Propagation Properties

Regularity of the Free Boundary for the One-Dimensional Flow of Gas in a Porous Medium

1979 ◽  
Vol 101 (6) ◽  
pp. 1193 ◽  
Author(s):  
Luis A. Caffarelli ◽  
Avner Friedman
Keyword(s):  
Porous Medium ◽  
Free Boundary ◽  
One Dimensional ◽  
Dimensional Flow ◽  
The One

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

scholarly journals On the one-dimensional flow of a conducting gas in crossed fields

1961 ◽  
Vol 19 (3) ◽  
pp. 177-193 ◽  
Author(s):  
Erling Dahlberg
Keyword(s):  
One Dimensional ◽  
Dimensional Flow ◽  
The One

Unsteady one-dimensional flow in a saturated porous medium with a volume heat source

1992 ◽  
Vol 26 (4) ◽  
pp. 572-580 ◽  
Author(s):  
Zyong Ngok Khai ◽  
R. I. Nigmatulin
Keyword(s):  
Porous Medium ◽  
Heat Source ◽  
Saturated Porous Medium ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Volume Heat

scholarly journals Asymptotics for a parabolic double obstacle problem

1994 ◽  
Vol 444 (1922) ◽  
pp. 429-445 ◽  
Keyword(s):  
Asymptotic Behaviour ◽  
Obstacle Problem ◽  
Thin Strip ◽  
Normal Velocity ◽  
One Dimensional ◽  
Cahn Equation ◽  
Small Constant ◽  
The One ◽  
Short Time ◽  
Double Well Potential

We consider a parabolic double obstacle problem which is a version of the Allen-Cahn equation u t = Δ u — ϵ -2 ψ '( u ) in Ω x (0, ∞), where Ω is a bounded domain, ϵ is a small constant, and ψ is a double well potential; here we take ψ such that ψ ( u ) = (1 — u 2 ) when | u | ≤ 1 and ψ ( u ) = ∞ when | u | > 1. We study the asymptotic behaviour, as ϵ → 0, of the solution of the double obstacle problem. Under some natural restrictions on the initial data, we show that after a short time (of order ϵ 2 |ln ϵ |), the solution takes value 1 in a region Ω + t and value — 1 in Ω - t , where the region Ω ( Ω + t U Ω - t ) is a thin strip and is contained in either a O ( ϵ |ln ϵ |) or O ( ϵ ) neighbourhood of a hypersurface Γ t which moves with normal velocity equal to its mean curvature. We also study the asymptotic behaviour, as t → ∞, of the solution in the one-dimensional case. In particular, we prove that the ω -limit set consists of a singleton.

SHOCK PROPAGATION IN A FLOW THROUGH DEFORMABLE POROUS MEDIA: ASYMPTOTIC BEHAVIOUR AS THE POROSITY APPROXIMATES A CONSTANT

2007 ◽  
Vol 17 (08) ◽  
pp. 1261-1278
Author(s):  
ELENA COMPARINI ◽  
MAURA UGHI
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Hydraulic Conductivity ◽  
Asymptotic Behaviour ◽  
Incompressible Flow ◽  
Shock Propagation ◽  
One Dimensional ◽  
Deformable Porous Media ◽  
Flux Intensity ◽  
Flow Through

We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered as functions of the flux intensity. We prove that if one approximates the porosity with a constant then the solution of the hyperbolic problem converges to the classical continuous Green–Ampt solution, also in the presence of shocks. In general, however, the shocks remain present in any approximating solution.

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