An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary

The deterministic and stochastic Wentzell systems of Barenblatt–Zheltov–Kochina equations describing moisture filtration in a three-dimensional ball and on its boundary are studied for the first time. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a specifically constructed Hilbert space is established. In the stochastic case, the Nelson–Glicklich derivative is used and a stochastic solution is constructed, which allows us to predict quantitative changes in the geochemical regime of groundwater under pressureless filtration. For the filtration system under study, the non-classical Wentzell condition was 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.