Geodesic
Stochastic Wentzel system of free fluid filtration equations on a hemisphere and on its edge
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 24-28

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Deterministic and stochastic Wentzell systems of the Dzekzer equations describing the evolution of the free surface of a filtering fluid in a hemisphere and at its edge are studied. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a particular constructed Hilbert space is established. In the case of the stochastic system, the theory of Nelson–Glicklich derivatives is used and a stochastic solution is constructed to quantify the change in the free filtration of the fluid.
Keywords: stochastic Dzekzer equation, system of Wentzell equations, the Nelson–Glicklich derivative. 
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     author = {N. S. Goncharov and G. A. Sviridyuk},
     title = {Stochastic {Wentzel} system of free fluid filtration equations on a hemisphere and on its edge},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     year = {2024},
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N. S. Goncharov; G. A. Sviridyuk. Stochastic Wentzel system of free fluid filtration equations on a hemisphere and on its edge. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 24-28. http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a2/