Mathematical Physics Porous Media Two-Phase Flow

Existence and Uniqueness of Nonmonotone Solutions in Porous Media Flow

R. Steinle, T. Kleiner, P. Kumar, R. Hilfer

Axioms 11, 327 (2022)

submitted on
Thursday, May 5, 2022

Existence and uniqueness of solutions for a simplified model of immiscible two-phase flow in porous media are obtained in this paper. The mathematical model is a simplified physical model with hysteresis in the flux functions. The resulting semilinear hyperbolic-parabolic equation is expected from numerical work to admit non-monotone imbibition-drainage fronts. We prove the local existence of imbibition-drainage fronts. The uniqueness, global existence, maximal regularity and boundedness of the solutions are also discussed. Methodically, the results are established by means of semigroup theory and fractional interpolation spaces.

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