Volume 17, no. 1Pages 86 - 96

Analysis of the Wentzell Stochastic System Composed of the Equations of Unpressurised Filtration in the Hemisphere and at Its Boundary

N.S. Goncharov, G.A. Sviridyuk
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.
Full text
Wentzell system; Dzekzer equation; Nelson-Glicklich derivative.
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