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.

Keywords

Wentzell system; Barenblatt-Zheltov-Kochina equation; Nelson-Glicklich derivative.

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