Abstract
In this paper we study the long-time dynamics of the perturbed system of suspension bridge equations
where \(\epsilon \in (0, 1]\) is a perturbed parameter and \(\gamma \in (0, 1)\) is said to be a fractional exponent. Under quite general assumptions on source terms and based on semigroup theory, we establish the global well-posedness and the existence of global attractors with finite fractal dimension. We analysis the upper semicontinuity of global attractors on the perturbed parameter \(\epsilon \) in some sense. Moreover, we demonstrate an explicit control over semidistances between trajectories in the weak energy phase space in terms of \(\epsilon \). Finally, we prove that the family of global attractors is upper semicontinuous with respect to the fractional exponent \(\gamma \in (0,1/2)\).
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The authors would like to thank the referees for their critical review and valuable comments which thoroughly improved the paper.
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Aouadi, M. Robustness of Global Attractors for Extensible Coupled Suspension Bridge Equations with Fractional Damping. Appl Math Optim 84 (Suppl 1), 403–435 (2021). https://doi.org/10.1007/s00245-021-09774-8
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DOI: https://doi.org/10.1007/s00245-021-09774-8
Keywords
- Extensible coupled suspension bridge
- Fractional damping
- Perturbations
- Global attractors
- Upper semicontinuity