Quasi-stability and continuity of attractors for nonlinear system of wave equations

Nonautonomous Dynamical Systems

Dos Santos M. J.¹  Freitas M. M.²  Ramos A. J. A.²  Santos M. L.³  Vinhote M. S.³ 

[1] Faculty of Exact Sciences and Technology, Federal University of Pará, Manoel de Abreu St, Abaetetuba, PA, 68440-000, Brazil;Faculty of Mathematics, Federal University of Pará, Raimundo Santana Cruz Street, S/N, 68721-000, Salinópolis, Pará, Brazil;PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street, 01, 66075-110, Belém, Pará, Brazil;

关键词: wave equations;    quasi-stable systems;    global attractor;    exponential attractor;    continuity of attractors;    35b40;    35b41;    35l05;    35l75;   

DOI  :  10.1515/msds-2020-0125

来源: DOAJ

【 摘 要 】

In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

【 授权许可】

Unknown