A degenerate parabolic system for three-phase flows in porous media
Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 2, p. 243-254

A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

@article{AMBP_2007__14_2_243_0,
     author = {Shelukhin, Vladimir},
     title = {A degenerate parabolic system for three-phase flows in porous media},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {14},
     number = {2},
     year = {2007},
     pages = {243-254},
     doi = {10.5802/ambp.234},
     mrnumber = {2369873},
     zbl = {1156.35393},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2007__14_2_243_0}
}
Shelukhin, Vladimir. A degenerate parabolic system for three-phase flows in porous media. Annales mathématiques Blaise Pascal, Volume 14 (2007) no. 2, pp. 243-254. doi : 10.5802/ambp.234. http://www.numdam.org/item/AMBP_2007__14_2_243_0/

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