Homogenization of a model of displacement with  unbounded viscosity

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

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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

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.
- Homogenization,
- nonlinear degenerate parabolic equations,
- coupled problem,
- porous media
Citation: Catherine Choquet, Ali Sili. Homogenization of a model of displacement with unbounded viscosity[J]. Networks and Heterogeneous Media, 2009, 4(4): 649-666. doi: 10.3934/nhm.2009.4.649

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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.
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