Stability results for a soil model with singular hysteretic hydrology

0360292 - MÚ 2012 RIV GB eng J - Journal Article
Krejčí, Pavel - O'Kane, J.P. - Pokrovskii, A. - Rachinskii, D.
Stability results for a soil model with singular hysteretic hydrology.
Journal of Physics: Conference Series. Roč. 268, č. 1 (2011), 012016. ISSN 1742-6588. E-ISSN 1742-6596.
[5th International workshop on multi-rate processes and hysteresis. Pecs, 31.05.2010-03.06.2010]
R&D Projects: GA ČR GAP201/10/2315
Institutional research plan: CEZ:AV0Z10190503
Keywords : hysteresis * evolution equation * stability
Subject RIV: BA - General Mathematics
http://iopscience.iop.org/1742-6596/268/1/012016

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 global asymptotic stability of periodic solutions.
Permanent Link: http://hdl.handle.net/11104/0197878