Homogenization of a model of displacement with  unbounded viscosity

Catherine Choquet; Ali Sili

doi:10.3934/nhm.2009.4.649

Article Contents

2009, Volume 4, Issue 4: 649-666. Doi: 10.3934/nhm.2009.4.649

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Homogenization of a model of displacement with unbounded viscosity

Catherine Choquet^1, and
Ali Sili^2,

1.
Université P. Cézanne, LATP, CNRS UMR 6632, FST, Case Cour A, 13397 Marseille Cedex 20
2.
Université de Toulon et du Var, Département de mathématiques, BP 20132, 83957 La Garde

Received: February 29, 2008

Revised: March 31, 2009

Published: November 2009

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Abstract

We discuss the homogenization of a model problem describing the transport of heat and mass by a compressible miscible flow in a highly heterogeneous porous medium. The flow is governed by a nonlinear system of degenerate parabolic type coupling the pressure and the temperature. Using the technique of two-scale convergence and compensated compactness arguments, we prove some stability in the homogenization process.

Keywords:

Homogenization,
nonlinear degenerate parabolic equations,
coupled problem,
porous media.

Mathematics Subject Classification: Primary: 76M50, 35K65; Secondary: 76S05, 35K55.

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