|
Transport of heat and mass in a fluid with vanishing mobility
Author(s):
Catherine
Choquet
Journal:
Quart. Appl. Math.
66
(2008),
771-779.
MSC (2000):
Primary 35K60, 35K65, 35B40, 76S05, 35K57.
Posted:
September 26, 2008
MathSciNet review:
2465144
Retrieve article in:
PDF
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.
References:
-
- 1.
- 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) - 2.
- 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) - 3.
- J. Bear.
Dynamics of Fluids in Porous Media. American Elsevier, 1972. - 4.
- 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) - 5.
- G. de Marsily.
Hydrogéologie quantitative. Masson, 1981. - 6.
- M. Kaviany.
Principles of heat transfer in porous media. Springer, 1999. - 7.
- 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) - 8.
- F. Murat.
Compacité par compensation. Ann. Scuola Norm. Sup. Pisa, 5:489-507, 1978. MR 506997 (80h:46043a) - 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.
- J. Simon.
Compact sets in the space . Ann. Math. Pura Appl., IV:65-96, 1987. MR 916688 (89c:46055) - 11.
- 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)
Similar Articles:
Retrieve articles in Quarterly of Applied Mathematics
with MSC
(2000):
35K60, 35K65, 35B40, 76S05, 35K57.
Retrieve articles in all Journals with MSC
(2000):
35K60, 35K65, 35B40, 76S05, 35K57.
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
PII:
S0033-569X-08-01085-4
Keywords:
Nonlinear degenerate parabolic system; compensated compactness; miscible compressible displacement; porous media.
Received by editor(s):
July 16, 2007
Posted:
September 26, 2008
Copyright of article:
Copyright
2008,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
|