One-dimensional two-phase generalized Forchheimer flows of incompressible fluids

Luan Hoang, Akif Ibraguimov, Thinh Kieu

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish
Pages (from-to)921-938
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - May 15 2013


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


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