Advances in Differential Equations

On a degenerate parabolic system for compressible, immiscible, two-phase flows in porous media

Cédric Galusinski and Mazen Saad

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The aim of this paper is to analyze a model of a degenerate nonlinear system arising from immiscible, compressible, two-phase, three-dimensional flows occurring in porous media. A degenerate weighted formulation is introduced to take into account the compressibility and the degeneracy. Two existence results of such a degenerate weak solution are introduced. The first result concerns the existence of solutions under a reasonable assumption on the capillary pressure. This condition allows the degeneracy only where one of the two phases is exclusively present. The second result establishes, for suitable initial data, the existence of solutions when the degeneracy occurs where one or the other phase is exclusively present. Nevertheless, for suitable initial data, a classical weak solution is obtained when the degeneracy is not too strong and occurs only where the injected phase is exclusively present.

Article information

Adv. Differential Equations, Volume 9, Number 11-12 (2004), 1235-1278.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations
Secondary: 35K50 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 76S05: Flows in porous media; filtration; seepage 76T99: None of the above, but in this section


Galusinski, Cédric; Saad, Mazen. On a degenerate parabolic system for compressible, immiscible, two-phase flows in porous media. Adv. Differential Equations 9 (2004), no. 11-12, 1235--1278.

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