Cílem projektu je úplná formulace hysterezního modelu filtrace v porézním prostředí, studium kvalitativního chování řešení, jeho existence a jednoznačnost. Numerické simulace získaných výstupů budou provedeny za spolupráce s University College Cork. (cs)
The poject will be related to pastial differential equations with hysteresis and will be applicable in hydrology. The full model describing flow through unsaturated porous media with proper boundary conditions will be derived. The resulting parabolic PDE with Preisach hysteresis under time derivative wiil be investigated with the intention to derive sufficient conditions for its well-posedness. The qualitative behaviour of solutions (stability, long time stabilization) in typical particular cases will be studied. Numerical simulations will be carried out in cooperation with University College Cork. (en)