Lin, G.G., Chen, L. and Wei, W. (2017) Random Attractors of the Stochastic Strongly Damped for the Higher-Order Nonlinear Kirchhoff-Type Equation. International Journal of Modern Nonlinear Theory and Application, 6, 59-69.
https://doi.org/10.4236/ijmnta.2017.62005

has been cited by the following article:

• TITLE: Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise

  AUTHORS: Guoguang Lin, Zhuoxi Li

  KEYWORDS: Stochastic Dynamical System, White Noise, Random Attractor Family, Wiener Process, Ornstein-Uhlenbeck Process

  JOURNAL NAME: Advances in Pure Mathematics, Vol.9 No.4, April 29, 2019

  ABSTRACT: The existence of random attractor family for a class of nonlinear high-order Kirchhoff equation stochastic dynamical systems with white noise is studied. The Ornstein-Uhlenbeck process and the weak solution of the equation are used to deal with the stochastic terms. The equation is transformed into a general stochastic equation. The bounded stochastic absorption set is obtained by estimating the solution of the equation and the existence of the random attractor family is obtained by isomorphic mapping method. Temper random compact sets of random attractor family are obtained.