Affiliations: [a] Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil. E-mails: [email protected], [email protected] | [b] Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abre Street, S/N, 68440-000, Abaetetuba, PA, Brazil. E-mail: [email protected] | [c] PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, Belém–PA, 66075-110, Brazil. E-mail: [email protected] | [d] Faculty of Petroleum Engineering, Federal University of Pará, Raimundo Santana Street, s/n, Salinópolis–PA, 68721-000, Brazil. E-mail: [email protected]
Abstract: We investigated the asymptotic dynamics of a nonlinear system modeling binary mixture of solids with delay term. Using the recent quasi-stability methods introduced by Chueshov and Lasiecka, we prove the existence, smoothness and finite dimensionality of a global attractor. We also prove the existence of exponential attractors. Moreover, we study the upper semicontinuity of global attractors with respect to small perturbations of the delay terms.
Keywords: Mixture of solids, time delay, quasi-stability, global attractors, upper-semicontinuity
