Asymptotic analysis and upper semicontinuity with respect to delay term of attractors to binary mixtures of solids-Reference-Cited by-同舟云学术

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

Published:2021-11-15 Issue: Volume: Page:1-26
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Freitas M.M.¹,Ramos A.J.A.¹,Dos Santos M.J.²,Miranda L.G.R.³,Almeida J.L.L.⁴

Affiliation:

1. Federal University of Pará, Raimundo Santana Street s/n, Salinópolis PA, 68721-000, Brazil. E-mails: mirelson@ufpa.br, ramos@ufpa.br

2. 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

3. PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, Belém–PA, 66075-110, Brazil. E-mail: luizmiranda@ufpa.br

4. Faculty of Petroleum Engineering, Federal University of Pará, Raimundo Santana Street, s/n, Salinópolis–PA, 68721-000, Brazil. E-mail: jammie.lud@gmail.com

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.

Publisher

IOS Press

Subject

General Mathematics

Reference36 articles.

1. Exponential decay in a thermoelastic mixture of solids;Alves;International Journal of Solids and Structures,2009

2. A.V. Babin and M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992.

3. A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials;Baer;International Journal of Multiphase Flow,1986

4. V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer Monographs in Mathematics, Vol. 190, Springer, New York, 2010.

5. Dissipative periodic processes;Billotti;Bull. Amer. Math. Soc.,1971