Geodesic
An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 4, pp. 84-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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N. S. Goncharov; G. A. Sviridyuk. An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 4, pp. 84-92. http://geodesic.mathdoc.fr/item/VYURU_2023_16_4_a5/

[1] Barenblatt G.I., Zheltov Iu.P., Kochina I.N., “Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks”, Journal of Applied Mathematics and Mechanics, 24:5 (1960), 1286–1303 | DOI | Zbl

[2] Goncharov N.S., Zagrebina S.A., Sviridyuk G.A., “Non-Uniqueness of Solutions to Boundary Value Problems with Wentzell Condition”, Bulletin of the South Ural State University. Series: Mathematical Modeling, Programming and Computer Software, 14:4 (2021), 102–105 | DOI | Zbl

[3] A. Favini, S.A. Zagrebina, G.A. Sviridyuk, “Multipoint Initial-Final Value Problem for Dynamical Sobolev-Type Equation in the Space of Noises”, Electronic Journal of Differential Equations, 2018:128 (2018), 1–10 | MR

[4] A. Favini, S.A. Zagrebina, G.A. Sviridyuk, “The Multipoint Initial-Final Value Condition for the Hoff Equations in Geometrical Graph in Spaces of K-«Noises»”, Mediterranean Journal of Mathematics, 19:2 (2022), 53 | DOI | MR | Zbl

[5] A. Favini, G.A. Sviridyuk, N.A. Manakova, “Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of «Noises»”, Abstract and Applied Analysis, 2015 (2015), 697410 | DOI | MR | Zbl

[6] A. Favini, G.A. Sviridyuk, A.A. Zamyshlyaeva, “One Class of Sobolev Type Equations of Higher Order with Additive «White Noise»”, Communications on Pure and Applied Analysis, 15:1 (2016), 185–196 | DOI | MR | Zbl

[7] A. Favini, G.A. Sviridyuk, M.A. Sagadeeva, “Linear Sobolev Type Equations with Relatively p-Radial Operators in Space of «Noises»”, Mediterranean Journal of Mathematics, 13:6 (2016), 4607–4621 | DOI | MR | Zbl

[8] J.L. Lions, E. Magenes, Problems aux limites non homogenes et applications, Dunod, Paris, 1968 | MR

[9] Goncharov N.S., Zagrebina S. A., Sviridyuk G. A., “The Showalter–Sidorov and Cauchy Problems for the Linear Dzekzer Equation with Wentzell and Robin Boundary Conditions in a Bounded Domain”, Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics, 14:1 (2022), 50–63 | DOI | Zbl

[10] Ventcel' A.D., “On Boundary Conditions for Multidimensional Diffusion Processes”, Theory of Probability and Its Applications, 4 (1959), 164–177 | DOI | MR

[11] Yu.E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, Theoretical and Mathematical Physics, Springer, London–Dordrecht–Heidelberg, 2011 | MR

[12] O.G. Kitaeva, D.E. Shafranov, G.A. Sviridyuk, “Exponential Dichotomies in Barenblatt – Zheltov – Kochina Model in Spaces of Differential Forms with «Noise»”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 12:2 (2019), 47–57 | DOI | Zbl

[13] N.S. Goncharov, “Stochastic Barenblatt – Zheltov – Kochina Model on the Interval with Wentzell Boundary Conditions”, Global and Stochastic Analysis, 7:1 (2020), 11–23