Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Transport of heat and mass in a fluid with vanishing mobility

Author: Catherine Choquet
Journal: Quart. Appl. Math. 66 (2008), 771-779
MSC (2000): Primary 35K60, 35K65, 35B40, 76S05, 35K57.
DOI: https://doi.org/10.1090/S0033-569X-08-01085-4
Published electronically: September 26, 2008
MathSciNet review: 2465144
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a model describing the compressible displacement of a mixture in a porous medium. The transport of heat and mass is described by a nonlinear, fully coupled and degenerate parabolic system. Using a series of compensated compactness and convexity arguments, we prove the existence of relevant weak solutions.

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  • 1. Y. Amirat, K. Hamdache, and A. Ziani, Mathematical analysis for compressible miscible displacement models in porous media, Math. Models Methods Appl. Sci. 6 (1996), no. 6, 729–747. MR 1404826, https://doi.org/10.1142/S0218202596000316
  • 2. Y. Amirat and A. Ziani, Asymptotic behavior of the solutions of an elliptic-parabolic system arising in flow in porous media, Z. Anal. Anwendungen 23 (2004), no. 2, 335–351. MR 2085294, https://doi.org/10.4171/ZAA/1202
  • 3. J. Bear.
    Dynamics of Fluids in Porous Media.
    American Elsevier, 1972.
  • 4. Catherine Choquet, Existence result for a radionuclide transport model with unbounded viscosity, J. Math. Fluid Mech. 6 (2004), no. 4, 365–388. MR 2101887, https://doi.org/10.1007/s00021-003-0097-z
  • 5. G. de Marsily.
    Hydrogéologie quantitative.
    Masson, 1981.
  • 6. M. Kaviany.
    Principles of heat transfer in porous media.
    Springer, 1999.
  • 7. Alexandre V. Kazhikhov, Recent developments in the global theory of two-dimensional compressible Navier-Stokes equations, Seminar on Mathematical Sciences, vol. 25, Keio University, Department of Mathematics, Yokohama, 1998. MR 1600212
  • 8. François Murat, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), no. 3, 489–507 (French). MR 506997
  • 9. M. Reeves and R.M. Cranwell.
    User's manual for the Sandia Waste-Isolation Flow and Transport model (SWIFT).
    Release 4.81. Sandia Report Nureg/Cr-2324, SAND81-2516, GF, Sandia National Laboratories, Albuquerque, 1981.
  • 10. Jacques Simon, Compact sets in the space 𝐿^{𝑝}(0,𝑇;𝐵), Ann. Mat. Pura Appl. (4) 146 (1987), 65–96. MR 916688, https://doi.org/10.1007/BF01762360
  • 11. L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, Boston, Mass.-London, 1979, pp. 136–212. MR 584398

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Additional Information

Catherine Choquet
Affiliation: Université P. Cézanne, FST, LATP-CNRS UMR 6632, Case Cour A, 13397 Marseille Cedex 20, France
Email: c.choquet@univ-cezanne.fr

DOI: https://doi.org/10.1090/S0033-569X-08-01085-4
Keywords: Nonlinear degenerate parabolic system; compensated compactness; miscible compressible displacement; porous media.
Received by editor(s): July 16, 2007
Published electronically: September 26, 2008
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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