Mitra, KoondanibhaSchweizer, BenRätz, Andreas2021-01-182021-01-182020-12http://hdl.handle.net/2003/39997http://dx.doi.org/10.17877/DE290R-21880We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.enporous mediahysteresistravelling waves610TextNumerische StrömungssimulationPoröser StoffWanderwelleSchwerkraftHysterese