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
Full-text PDF Free Access
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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.
References
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- François Murat, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), no. 3, 489–507 (French). MR 506997
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References
- Y. Amirat, K. Hamdache, and A. Ziani. Mathematical analysis for compressible miscible displacement models in porous media. Math. Models Methods Appl. Sci., 6(6):729–747, 1996. MR 1404826 (97g:76086)
- Y. Amirat and A. Ziani. Asymptotic behavior of the solutions of an elliptic-parabolic system arising in flow in porous media. Z. Anal. Andwendungen, 23(2):335–351, 2004. MR 2085294 (2007d:35215)
- J. Bear. Dynamics of Fluids in Porous Media. American Elsevier, 1972.
- C. Choquet. Existence result for a radionuclide transport model with an unbounded viscosity. J. Math. Fluid Mech., 6(4):365–388, 2004. MR 2101887 (2005m:35142)
- G. de Marsily. Hydrogéologie quantitative. Masson, 1981.
- M. Kaviany. Principles of heat transfer in porous media. Springer, 1999.
- A.V. Kazhikhov. Recent developments in the global theory of two-dimensional compressible Navier-Stokes equations. Seminar on Mathematical Sciences, Keio University, 25, 1998. MR 1600212 (98k:35150)
- F. Murat. Compacité par compensation. Ann. Scuola Norm. Sup. Pisa, 5:489–507, 1978. MR 506997 (80h:46043a)
- 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.
- J. Simon. Compact sets in the space ${L}^p(0,{T};{B})$. Ann. Math. Pura Appl., IV:65–96, 1987. MR 916688 (89c:46055)
- L. Tartar. Compensated compactness and applications to P.D.E. In R.J. Knops, editor, Non Linear Analysis and Mechanics, Heriot-Watt Symposium, Research Notes in Math., volume 4 (39), pages 136–212. Pitman Press, 1979. MR 584398 (81m:35014)
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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
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.
