Author(s)

Guoguang Lin, Zhuoxi Li

Department of Mathematics, Yunnan University, Kunming, China.

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.

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

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