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Global attractors of coupled suspension bridge equations with nonlocal weak damping term. (Chinese. English summary) Zbl 1474.35126

Summary: We investigate the long-time dynamical behavior of coupled suspension bridge equations with nonlocal weak damping term. Firstly, we establish the well-posedness of the solutions based on the monotone operator theory. Secondly, the dissipation of solution semigroup \(\{S (t)\}_{t \ge 0}\) is obtained. Then the asymptotic smoothness of the solution semigroup \(\{S (t)\}_{t \ge 0}\) is verified by the energy reconstruction method. Finally the existence of global attractors for the coupled suspension bridge equations with nonlocal weak damping term is proved.

MSC:

35B41 Attractors
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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