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Lin, G.G. and Li, Z.X. (2019) Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise. Advances in Pure Mathematics, 9, 404-414.
https://doi.org/10.4236/apm.2019.94018

has been cited by the following article:

• TITLE: A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations

  AUTHORS: Guoguang Lin, Lujiao Yang

  KEYWORDS: Stochastic Kirchhoff Equation, A Family of the Random Attractors, Multiplicative White Noise, Ornstein-Uhlenbeck Process

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.11, November 26, 2021

  ABSTRACT: In this paper, we studied the existence of a family of the random attractor for a class of generalized Kirchhoff-type equations with a strong dissipation term. Firstly, according to Ornstein-Uhlenbeck process, we transformed the equation into a stochastic equation with random variables and multiplicative white noise. Secondly, we proved the existence of a bounded random absorbing set. Finally, by using the isomorphic mapping method and the compact embedding theorem, we get the stochastic dynamical system with a family of random attractors.