Geodesic
Stability of solutions to the stochastic Oskolkov equation and stabilization
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 1, pp. 17-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies the stability of solutions to the stochastic Oskolkov equation describing a plane-parallel flow of a viscoelastic fluid. This is the equation we consider in the form of a stochastic semilinear Sobolev type equation. First, we consider the solvability of the stochastic Oskolkov equation by the stochastic phase space method. Secondly, we consider the stability of solutions to this equation. The necessary conditions for the existence of stable and unstable invariant manifolds of the stochastic Oskolkov equation are proved. When solving the stabilization problem, this equation is considered as a reduced stochastic system of equations. The stabilization problem is solved on the basis of the feedback principle; graphs of the solution before stabilization and after stabilization are shown.
Keywords: the Oskolkov equation, stochastic Sobolev-type equations, invariant manifolds, the stabilization problem. 
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O. G. Kitaeva. Stability of solutions to the stochastic Oskolkov equation and stabilization. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 1, pp. 17-26. http://geodesic.mathdoc.fr/item/VYURU_2024_17_1_a1/

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