A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations ()
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.
Share and Cite:
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.
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