On a degenerate parabolic system for compressible, immiscible, two-phase flows in porous media. (English) Zbl 1102.35342

Galusinski, Cédric; Saad, Mazen

Adv. Differ. Equ. 9, No. 11-12, 1235-1278 (2004).

A degenerate nonlinear system modelling a three-dimensional displacement of two immiscible, compressible fluids in a porus medium is studied. The main results of the paper are two existence results of degenerate weak solutions. The existence of a classical weak solution is also discussed.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

35K65	Degenerate parabolic equations
35K57	Reaction-diffusion equations
35K50	Systems of parabolic equations, boundary value problems (MSC2000)
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76S05	Flows in porous media; filtration; seepage
76T99	Multiphase and multicomponent flows
35D05	Existence of generalized solutions of PDE (MSC2000)

Keywords:

parabolic system; degenerate weak solutions; compressible fluids; porous medium; two existence results