Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 797-812 |
| Journal | IMA Journal of Applied Mathematics |
| Volume | 84 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2019 |
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Traveling wave solutions for the Richards equation with hysteresis. / Behi-Gornostaeva, E.E.; Mitra, K.; Schweizer, B. (Corresponding author).
In: IMA Journal of Applied Mathematics, Vol. 84, No. 4, 08.2019, p. 797-812.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Traveling wave solutions for the Richards equation with hysteresis
AU - Behi-Gornostaeva, E.E.
AU - Mitra, K.
AU - Schweizer, B.
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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.
U2 - 10.1093/imamat/hxz015
DO - 10.1093/imamat/hxz015
M3 - Article
VL - 84
SP - 797
EP - 812
JO - IMA Journal of Applied Mathematics
JF - IMA Journal of Applied Mathematics
SN - 0272-4960
IS - 4
ER -