WIAS Preprint No. 1341, (2008)

Stability results for a soil model with singular hysteretic hydrology


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • O'Kane, J. Philip
  • Pokrovskii, Alexei
  • Rachinskii, Dmitrii

2010 Mathematics Subject Classification

  • 34C55 34C25 76S05


  • Preisach operator, singular differential equation, periodic solution




We consider a differential equation describing the mass balance in a soil hydrology model with noninvertible Preisach-type hysteresis. We approximate the singular Preisach operator by regular ones and show, as main result, that the solutions of the regularized problem converge to a solution of the original one as the regularization parameter tends to zero. For monotone right hand sides, we prove that the solution is unique. If in addition the external water sources are time periodic, then we find sufficient conditions for the existence, uniqueness, and asymptotic stability of periodic solutions.

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