El Behi-Gornostaeva, ElenaMitra, KoondanibhaSchweizer, Ben2019-01-082019-01-082018-09-24http://hdl.handle.net/2003/37863http://dx.doi.org/10.17877/DE290R-19850We investigate the one-dimensional non-equilibrium Richards equation with play-type hysteresis. It is known that regularized versions of this equation permit traveling wave solutions that show oscillations and, in particular, the physically relevant effect of a saturation overshoot. We investigate here the non-regularized hysteresis operator and combine it with a positive τ-term. Our result is that the model has monotone traveling wave solutions. These traveling waves describe the behavior of fronts in a bounded domain. In a two-dimensional interpretation, the result characterizes the speed of fingers in non-homogeneous solutions.enporous mediahysteresistraveling wavesaturation overshoot610Text