%0 Journal Article
%T Random Attractor Family for the Kirchhoff Equation of Higher Order with White Noise
%A Guoguang Lin
%A Zhuoxi Li
%J Advances in Pure Mathematics
%P 404-414
%@ 2160-0384
%D 2019
%I Scientific Research Publishing
%R 10.4236/apm.2019.94018
%X 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 </span><span style=\"font-family:Verdana;\">is</span><span style=\"font-family:Verdana;\"> obtained by isomorphic mapping method. Temper random compact sets of
random attractor family are obtained.
%K Stochastic Dynamical System
%K White Noise
%K Random Attractor Family
%K Wiener Process
%K Ornstein-Uhlenbeck Process
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=92180