Traveling wave solutions for the Richards equation with hysteresis

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

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
87 Downloads (Pure)


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 nonregularized hysteresis operator and combine it with a positive t -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
Number of pages16
JournalIMA Journal of Applied Mathematics
Issue number4
Publication statusPublished - 1 Aug 2019


  • hysteresis
  • porous media
  • saturation overshoot
  • traveling wave


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