Geodesic
Stabilization of the stochastic Barenblatt~-- Zheltov~-- Kochina equation
Journal of computational and engineering mathematics, Tome 10 (2023) no. 1, pp. 21-29.

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The article is devoted to the stabilization of solutions to the stochastic Barenblatt – Zheltov – Kochina equation. The Barenblatt – Zheltov – Kochina equation is a model of filtration of a viscous liquid in a porous medium. This equation also models the processes of moisture transfer in the soil. We consider the problem for the Barenblatt – Zheltov – Kochina equation with random initial data. The equation is considered as a system of equations given on stable and unstable invariant spaces. The problem of stabilization is as follows. It is required to find a controlling effect on the system so that its solutions become asymptotically stable. For the stochastic Barenblatt – Zheltov – Kochina equation, we find feedback such that the closed system is asymptotically stable. Numerical solutions to the stochastic Barenblatt – Zheltov – Kochina equation and the stabilized equation are found. Graphs of solutions are constructed.
Keywords: stochastic Sobolev type equations, stable and unstable invariant spaces, stabilization of solutions. 
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     author = {O. G. Kitaeva},
     title = {Stabilization of the stochastic {Barenblatt~--} {Zheltov~--} {Kochina} equation},
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     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2023_10_1_a2/}
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O. G. Kitaeva. Stabilization of the stochastic Barenblatt~-- Zheltov~-- Kochina equation. Journal of computational and engineering mathematics, Tome 10 (2023) no. 1, pp. 21-29. http://geodesic.mathdoc.fr/item/JCEM_2023_10_1_a2/