Global attractors of coupled suspension bridge equations with nonlocal weak damping terms

Abstract:

We investigate the long-time dynamical behavior of coupled suspension bridge equations with nonlocal weak damping terms. Firstly, we establish the well-posedness of the solutions based on the monotone operator theory. Secondly, the dissipation of solution semigroups {S(t)} is obtained. Then the asymptotic smoothness of solution semigroups {S(t)} is verified by using the energy reconstruction method. Fianlly the existence of global attractors for the coupled suspension bridge equations with nonlocal weak damping terms is proved.