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 -