Steinle, RouvenKleiner, TillmannKumar, PradeepHilfer, Rudolf2023-01-192023-01-1920222075-16801831837439http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-126795http://elib.uni-stuttgart.de/handle/11682/12679http://dx.doi.org/10.18419/opus-12660Existence 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.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/530article2022-08-03