Nonsteady flow of water and oil through inhomogeneous porous media

H. W. Alt; E. Di Benedetto

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)

  • Volume: 12, Issue: 3, page 335-392
  • ISSN: 0391-173X

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Alt, H. W., and Di Benedetto, E.. "Nonsteady flow of water and oil through inhomogeneous porous media." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.3 (1985): 335-392. <http://eudml.org/doc/83960>.

@article{Alt1985,
author = {Alt, H. W., Di Benedetto, E.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {nonlinear partial differential equations; two immiscible fluids; porous medium; degenerate elliptic-parabolic equations},
language = {eng},
number = {3},
pages = {335-392},
publisher = {Scuola normale superiore},
title = {Nonsteady flow of water and oil through inhomogeneous porous media},
url = {http://eudml.org/doc/83960},
volume = {12},
year = {1985},
}

TY - JOUR
AU - Alt, H. W.
AU - Di Benedetto, E.
TI - Nonsteady flow of water and oil through inhomogeneous porous media
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 3
SP - 335
EP - 392
LA - eng
KW - nonlinear partial differential equations; two immiscible fluids; porous medium; degenerate elliptic-parabolic equations
UR - http://eudml.org/doc/83960
ER -

References

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  1. [1] H.W. Alt - S. Luckhaus, Quasilinear elliptic -parabolic differential equations, Preprint 136, SFB 123, Heidelberg, and Math. Z., 183 (1983), pp. 311-341. Zbl0497.35049MR706391
  2. [2] J. Bear, Dynamics of fluids in porous media, American Elsevier, New York, 1972. Zbl1191.76001
  3. [3] J. Bear, Hydraulics of Groundwater, Mc-Graw Hill, New York, 1979. 
  4. [4] R.E. Collins, Flow of fluids through porous materials, Reinhold, New York, 1961. 
  5. [5] E. Dibenedetto, Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl., (IV), 130 (1982), pp. 131-177. Zbl0503.35018MR663969
  6. [6] J. DouglasJr., Finite difference methods for two-phase incompressible flow in porous media, Siam J. Numer. Anal., 20 (1983), pp. 681-696. Zbl0519.76107MR708451
  7. [7] J. DouglasJr. - B.L. Darlow - M.F. Wheeler - R.P. Kendall, Self-adaptive finite element and finite difference methods for two-phase immiscible flow, to appear. 
  8. [8] J. Glimm - D. Marchesin - O. McBRYAN, Unstable fingers in two phase flow, Comm. Pure Appl. Math., 34 (1981), pp. 53-76. Zbl0469.76078MR600572
  9. [9] D. Kröner - S. Luckhaus, Flow of oil and water in a porous medium, J. Differential Equations, 55 (1984), pp. 276-288. Zbl0509.35048MR764127
  10. [10] S.N. Kruzkov - S.M. Sukorjanski, Boundary value problems for systems of equations of two phase porous flow type: statement of the problems, questions of solvability, justification of approximate methods, Mat. Sb., 33 (1977), pp. 62-80. Zbl0398.35039
  11. [11] O.A. Ladyzenskaja - N.N. Urel'tzeva, Linear and quasi-linear equations of elliptic type, Academic Press, New York (1968). 
  12. [12] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'tzeva, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc. Transl. Math. Mono, vol. 23 (Providence, R.I., 1968). Zbl0174.15403
  13. [13] M.C. Leverett, Capillary behavior in porous solids, Trans. Amer. Inst. Mining and Metallurgical Engrs., 142 (1941), pp. 152-169. 
  14. [14] A.E. Scheidegger, The Physics of flow through porous media, 3rd ed., Univ. of Toronto Press, Toronto, Ontario, 1974. Zbl0095.22402
  15. [15] A. Spivak - H.S. Price - A. Settari, Solution of the equations for multidimensional, two-phase, immiscible flow by variational methods, Soc. Pet. Eng. J., Feb. 1977, pp. 27-41. 

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