Analysis of the Wentzell Stochastic System Composed of the Equations of Unpressurised Filtration in the Hemisphere and At Its Boundary
Goncharov, N.S., Sviridyuk, G.A., Гончаров, Н.С., Свиридюк, Г.А. · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · 2024
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 "reservoirwell-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.