Traveling wave solutions for the Richards equation with hysteresis
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Date
2018-09-24
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Abstract
We 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.
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porous media, hysteresis, traveling wave, saturation overshoot