Existence and continuity of global attractors for ternary mixtures of solids

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula>, inspired by the modelstudied by Dell' Oro and Rivera [<xref ref-type="bibr" rid="b12">12</xref>]. We establish astabilizability estimate for the associated gradient dynamicalsystem, which as a consequence, implies the existence of a compactglobal attractor with finite fractal dimension andexponential attractors. This estimate is establishedindependent of the parameter <inline-formula><tex-math id="M2">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. We also prove thesmoothness of global attractors independent of the parameter<inline-formula><tex-math id="M3">\begin{document}$ \epsilon\in[0,1] $\end{document}</tex-math></inline-formula>. Moreover, we show that the family of globalattractors is continuous with respect to the parameter <inline-formula><tex-math id="M4">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> ona residual dense set <inline-formula><tex-math id="M5">\begin{document}$ I_*\subset[0,1] $\end{document}</tex-math></inline-formula> in the same sense proposed inHoang et al. [<xref ref-type="bibr" rid="b15">15</xref>].</p>