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 $D_k-$absorbing sets in the stochastic dynamical system ${\Phi }_k$, and the asymptotic compactness of ${\Phi }_k$ is proved via decomposition. Finally, the family of $D_k-$random attractors is acquired for the stochastic dynamical system ${\Phi }_k$ in $V_{m+k}\left(\Omega \right)\times V_{m+k}^{b_0}\left(\Omega \right)$. 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.