Stochastic Wentzel system of free fluid filtration equations on a hemisphere and on its edge

Deterministic and stochastic Wentzell systems of the Dzekzer equations describing the evolution of the free surface of a filtering fluid in a hemisphere and at its edge are studied. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a particular constructed Hilbert space is established. In the case of the stochastic system, the theory of Nelson–Glicklich derivatives is used and a stochastic solution is constructed to quantify the change in the free filtration of the fluid.