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.