Geodesic
Invariant manifolds of the Hoff model in “noise” spaces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 24-35

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The work is devoted to the study the stochastic analogue of the Hoff equation, which is a model of the deviation of an I-beam from the equilibrium position. The stability of the model is shown for some values of the parameters of this model. In the study, the model is considered as a stochastic semilinear Sobolev type equation. The obtained results are transferred to the Hoff equation, considered in specially constructed “noise” spaces. It is proved that, in the vicinity of the zero point, there exist finite-dimensional unstable and infinite-dimensional stable invariant manifolds of the Hoff equation with positive values of parameters characterizing the properties of the beam material and the load on the beam.
Keywords: the Nelson–Gliklikh derivative, stochastic Sobolev type equations, invariant manifolds. 
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     author = {O. G. Kitaeva},
     title = {Invariant manifolds of the {Hoff} model in {\textquotedblleft}noise{\textquotedblright} spaces},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {24--35},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a1/}
}
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O. G. Kitaeva. Invariant manifolds of the Hoff model in “noise” spaces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 24-35. http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a1/