Asymptotic analysis and upper semicontinuity with respect to delay term of attractors to binary mixtures of solids

Article type: Research Article

Authors: Freitas, M.M.^{a; *} | Ramos, A.J.A.^a | Dos Santos, M.J.^b | Miranda, L.G.R.^c | Almeida, J.L.L.^d

Affiliations: [a] Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil. E-mails: mirelson@ufpa.br, ramos@ufpa.br | [b] Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abre Street, S/N, 68440-000, Abaetetuba, PA, Brazil. E-mail: jeremias@ufpa.br | [c] PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, Belém–PA, 66075-110, Brazil. E-mail: luizmiranda@ufpa.br | [d] Faculty of Petroleum Engineering, Federal University of Pará, Raimundo Santana Street, s/n, Salinópolis–PA, 68721-000, Brazil. E-mail: jammie.lud@gmail.com

Correspondence: [*] Corresponding author. E-mail: mirelson@ufpa.br.

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

DOI: 10.3233/ASY-211739

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 519-544, 2022