Asymptotic behavior of a Balakrishnan-Taylor suspension bridge

Zayd Hajjej; Zayd Hajjej

doi:10.3934/era.2024075

Electronic Research Archive

2024, Volume 32, Issue 3: 1646-1662. doi: 10.3934/era.2024075

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Asymptotic behavior of a Balakrishnan-Taylor suspension bridge

Zayd Hajjej ^,

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 11 October 2023 Revised: 08 January 2024 Accepted: 11 January 2024 Published: 19 February 2024

In this manuscript, we examine a nonlinear Cauchy problem aimed at describing the deformation of the deck of either a footbridge or a suspension bridge in a rectangular domain $ \Omega = (0, \pi)\times (-d, d) $, with $ d < < \pi $, incorporating hinged boundary conditions along its short edges, as well as free boundary conditions along its remaining free edges. We establish the existence of solutions and the exponential decay of energy.
- Balakrishnan-Taylor suspension bridge,
- existence of solutions,
- exponential decay
Citation: Zayd Hajjej. Asymptotic behavior of a Balakrishnan-Taylor suspension bridge[J]. Electronic Research Archive, 2024, 32(3): 1646-1662. doi: 10.3934/era.2024075

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Abstract

In this manuscript, we examine a nonlinear Cauchy problem aimed at describing the deformation of the deck of either a footbridge or a suspension bridge in a rectangular domain $ \Omega = (0, \pi)\times (-d, d) $, with $ d < < \pi $, incorporating hinged boundary conditions along its short edges, as well as free boundary conditions along its remaining free edges. We establish the existence of solutions and the exponential decay of energy.

References

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