## Abstract

We derive a nonlinear system of parabolic equations to describe the one-dimensional two-phase generalized Forchheimer flows of incompressible, immiscible fluids in porous media, with the presence of capillary forces. Under relevant constraints on relative permeabilities and capillary pressure, non-constant steady state solutions are found and classified into sixteen types according to their monotonicity and asymptotic behavior. For a steady state whose saturation can never attain either value 0 or 1, we prove that it is stable with respect to a certain weight. This weight is a function comprised of the steady state, relative permeabilities and capillary pressure. The proof is based on specific properties of the steady state, weighted maximum principle and Bernstein's estimate.

Original language | English |
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Pages (from-to) | 921-938 |

Number of pages | 18 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 401 |

Issue number | 2 |

DOIs | |

State | Published - May 15 2013 |

## Keywords

- Forchheimer
- Porous media
- Stability
- Two-phase ows