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

Abstract

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.

Keywords

• wave equations
• quasi-stable systems
• global attractor
• exponential attractor
• continuity of attractors
• 35b40
• 35b41
• 35l05
• 35l75