# American Institute of Mathematical Sciences

May  2021, 26(5): 2805-2828. doi: 10.3934/dcdsb.2020206

## Global and exponential attractors for a nonlinear porous elastic system with delay term

 1 Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abreu St., Abaetetuba, Pará, 68440-000, Brazil 2 Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China 3 PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa St., 01, 66075-110, Belém - Pará - Brazil

* Corresponding author: Manoel J. Dos Santos

Received  July 2019 Revised  May 2020 Published  July 2020

This paper is concerned with the study on the existence of attractors for a nonlinear porous elastic system subjected to a delay-type damping in the volume fraction equation. The study will be performed, from the point of view of quasi-stability for infinite dimensional dynamical systems and from then on we will have the result of the existence of global and exponential attractors.

Citation: Manoel J. Dos Santos, Baowei Feng, Dilberto S. Almeida Júnior, Mauro L. Santos. Global and exponential attractors for a nonlinear porous elastic system with delay term. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2805-2828. doi: 10.3934/dcdsb.2020206
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