Author(s)

Guoguang Lin, Lujiao Yang

Department of Mathematics, Yunnan University, Kunming, China.

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.

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

Lin, G. and Yang, L. (2021) A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations. Journal of Applied Mathematics and Physics, 9, 2966-2978. doi: 10.4236/jamp.2021.911190.