Existence and continuity of global attractors for ternary mixtures of solids

In this paper, we study the long-time dynamics of a system modelinga mixture of three interacting continua with nonlinear damping, sources terms and subjected to small perturbations of autonomousexternal forces with a parameter \begin{document}$ \epsilon $\end{document} , inspired by the modelstudied by Dell' Oro and Rivera [ 12 ]. We establish astabilizability estimate for the associated gradient dynamicalsystem, which as a consequence, implies the existence of a compactglobal attractor with finite fractal dimension andexponential attractors. This estimate is establishedindependent of the parameter \begin{document}$ \epsilon\in[0,1] $\end{document} . We also prove thesmoothness of global attractors independent of the parameter \begin{document}$ \epsilon\in[0,1] $\end{document} . Moreover, we show that the family of globalattractors is continuous with respect to the parameter \begin{document}$ \epsilon $\end{document} ona residual dense set \begin{document}$ I_*\subset[0,1] $\end{document} in the same sense proposed inHoang et al. [ 15 ].