Traveling wave solutions for the Richards equation with hysteresis

E.E. Behi-Gornostaeva, K. Mitra, B. Schweizer (Corresponding author)

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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 $\tau$-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.
Original languageEnglish
Pages (from-to)797-812
JournalIMA Journal of Applied Mathematics
Volume84
Issue number4
DOIs
Publication statusPublished - Aug 2019

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Richards Equation
Traveling Wave Solutions
Hysteresis
Hysteresis Operators
Overshoot
Traveling Wave
Non-equilibrium
Saturation
Bounded Domain
Monotone
Oscillation
Term
Model
Interpretation

Cite this

Behi-Gornostaeva, E.E. ; Mitra, K. ; Schweizer, B. / Traveling wave solutions for the Richards equation with hysteresis. In: IMA Journal of Applied Mathematics. 2019 ; Vol. 84, No. 4. pp. 797-812.
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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 journalArticleAcademicpeer-review

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AU - Mitra, K.

AU - Schweizer, B.

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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.

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