Long-time dynamics of a random higher-order Kirchhoff model with variable coefficient rotational inertia

Abstract

This paper delves into the stochastic asymptotic behavior of a non-autonomous stochastic higher-order Kirchhoff equation with variable coefficient rotational inertia. The equation is solved using the Galerkin method, and a stochastic dynamical system is established on this basis. Uniform estimation demonstrates a family of Dk−absorbing sets in the stochastic dynamical system Φk, and the asymptotic compactness of Φk is proved via decomposition. Finally, the family of Dk−random attractors is acquired for the stochastic dynamical system Φk in Vm+k(Ω)×Vm+kb0(Ω). These results improve and extend those in recent literature (Lv et al., 2021). The findings promote the relevant conclusions of the non-autonomous stochastic higher-order Kirchhoff model and provide a theoretical basis for its subsequent application and research.

Keywords

• Non-autonomous higher-order Kirchhoff equation
• Variable coefficient rotational inertia
• Random attractor family