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
    F. Murat, Compacité par compensation. II, Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978) Pitagora, Bologna, 1979, pp. 245–256 (French). MR 533170
  • 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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