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Existence of Random Attractor Family for a Class of Nonlinear Higher-Order Kirchhoff Equations

DOI: 10.4236/ijmnta.2019.82003, PP. 41-52

Keywords: Stochastic Dynamical Systems, Random Attractor Family, White Noise, Ornstein-Uhlenbeck Process, Tempered Sets

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Abstract:

The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.

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