### STABILIZATION OF THE STOCHASTIC BARENBLATT -- ZHELTOV -- KOCHINA EQUATION

#### Abstract

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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