Invariant Manifolds of the Hoff Model in "Noise" Spaces
Copyright policy )Invariant Manifolds of the Hoff Model in "Noise" Spaces
Summary: 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.
- South Ural State University (Южно-Уральский государственный университет) Russian Federation
invariant manifolds, Initial value problems for PDEs with pseudodifferential operators, УДК 517.9, stochastic Sobolev type equations, инвариантные многообразия, finite-dimensional unstable manifold, infinite-dimensional stable invariant manifold, стохастические уравнения соболевского типа, Nelson-Gliklikh derivative, Initial-boundary value problems for second-order parabolic equations, PDEs with randomness, stochastic partial differential equations, производная Нельсона – Гликлиха, the Nelson–Gliklikh derivative, Ultraparabolic equations, pseudoparabolic equations, etc.
invariant manifolds, Initial value problems for PDEs with pseudodifferential operators, УДК 517.9, stochastic Sobolev type equations, инвариантные многообразия, finite-dimensional unstable manifold, infinite-dimensional stable invariant manifold, стохастические уравнения соболевского типа, Nelson-Gliklikh derivative, Initial-boundary value problems for second-order parabolic equations, PDEs with randomness, stochastic partial differential equations, производная Нельсона – Гликлиха, the Nelson–Gliklikh derivative, Ultraparabolic equations, pseudoparabolic equations, etc.
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