Analysis of the Wentzell stochastic system composed of the equations of unpressurised filtration in the hemisphere and at its boundary

The deterministic and stochastic Wentzell systems of Dzekzer equations in a hemisphere and on its boundary are studied for the first time. The deterministic case is characterised by the unambiguous solvability of the initial problem for the Wentzell system in a specific constructed Hilbert space. In the case of the stochastic hydrodynamic system “reservoir-well-collector”, the theory of Nelson–Glicklich derivative is applied and a stochastic solution is constructed, which allows us to determine the prognoses of quantitative changes in the geochemical regime of groundwater under non-pressure filtration. It should be noted that for the filtration system under study, the non-classical Wentzell condition is considered, since it is represented by an equation with the Laplace – Beltrami operator defined on the boundary of the domain, understood as a smooth compact Riemannian manifold without an edge, and the external influence is represented by the normal derivative of the function defined in the domain.