Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media

Y. Amirat; A. Ziani

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 1, page 109-128
  • ISSN: 0392-4041

Abstract

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We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing to compensated compactness arguments.

How to cite

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Amirat, Y., and Ziani, A.. "Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 109-128. <http://eudml.org/doc/195681>.

@article{Amirat2004,
abstract = {We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing to compensated compactness arguments.},
author = {Amirat, Y., Ziani, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {a priori estimates; viscosity type solutions; compensated compactness},
language = {eng},
month = {2},
number = {1},
pages = {109-128},
publisher = {Unione Matematica Italiana},
title = {Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media},
url = {http://eudml.org/doc/195681},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Amirat, Y.
AU - Ziani, A.
TI - Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 109
EP - 128
AB - We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing to compensated compactness arguments.
LA - eng
KW - a priori estimates; viscosity type solutions; compensated compactness
UR - http://eudml.org/doc/195681
ER -

References

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  14. PEARSON, J. R. A.- TARDY, P. M. J., Models for flow of non-Newtonian and complex fluids through porous media, J. Non-Newtonian Fluid Mech., 102 (2002), 447-473. Zbl0997.76006
  15. SCHEIDEGGER, A. E., The Physics of flow through porous media (Univ. Toronto Press, 1974). Zbl0095.22402
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