Browsing by Author "Kumar, Pradeep"

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    Existence and uniqueness of nonmonotone solutions in porous media flow
    (2022) Steinle, Rouven; Kleiner, Tillmann; Kumar, Pradeep; Hilfer, Rudolf
    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.