TITLE:
A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations
AUTHORS:
Guoguang Lin, Lujiao Yang
KEYWORDS:
Stochastic Kirchhoff Equation, A Family of the Random Attractors, Multiplicative White Noise, Ornstein-Uhlenbeck Process
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.11,
November
26,
2021
ABSTRACT: 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.