Stability results for a soil model with singular hysteretic hydrology

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.

Keywords

Preisach operator, singular differential equation, periodic solution

URI

https://doi.org/10.34657/3251
https://oa.tib.eu/renate/handle/123456789/2001

Citation

Krejčí, P., O’Kane, J. P., Pokrovskii, A., & Rachinskii, D. (2008). Stability results for a soil model with singular hysteretic hydrology (Vol. 1341). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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