Stability results for a soil model with singular hysteretic hydrology

0360292 - MÚ 2012 RIV GB eng J - Článek v odborném periodiku
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]
Grant CEP: GA ČR GAP201/10/2315
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: hysteresis * evolution equation * stability
Kód oboru RIV: BA - Obecná matematika
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.
Trvalý link: http://hdl.handle.net/11104/0197878