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JOURNALS // Journal of Computational and Engineering Mathematics // Archive

J. Comp. Eng. Math., 2023 Volume 10, Issue 1, Pages 21–29 (Mi jcem230)

This article is cited in 3 papers

Computational Mathematics

Stabilization of the stochastic Barenblatt – Zheltov – Kochina equation

O. G. Kitaeva

South Ural State University, Chelyabinsk, Russian Federation

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.

UDC: 517.9

MSC: 35G05

Received: 01.03.2023

Language: English

DOI: 10.14529/jcem230103



© Steklov Math. Inst. of RAS, 2024