Traveling wave solutions for the Richards equation with hysteresis

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 h...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 84; no. 4; pp. 797 - 812
Main Authors Behi-Gornostaeva, E El, Mitra, K, Schweizer, B
Format Journal Article
LanguageEnglish
Published 01.08.2019
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Summary: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 $\tau $-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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxz015