A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time

Zayd Hajjej; Zayd Hajjej

doi:10.3934/math.20241070

AIMS Mathematics

2024, Volume 9, Issue 8: 22022-22040. doi: 10.3934/math.20241070

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Research article

A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time

Zayd Hajjej ^,

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

Received: 04 June 2024 Revised: 04 July 2024 Accepted: 08 July 2024 Published: 12 July 2024
MSC : 26A33, 35B44, 74K20, 93D23

In the present paper, we examine a suspension bridges model subject to frictional damping, a fractional delay term, and a source term. First, we prove the existence of global solutions of the problem. Second, for small initial data, we establish the exponential stability of the system by using the energy method. Additionally, we show that if the initial energy assumes a negative value, the solution blows up in finite time.
- suspension bridges,
- fractional delay,
- exponential stability,
- blow-up
Citation: Zayd Hajjej. A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time[J]. AIMS Mathematics, 2024, 9(8): 22022-22040. doi: 10.3934/math.20241070

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Abstract

In the present paper, we examine a suspension bridges model subject to frictional damping, a fractional delay term, and a source term. First, we prove the existence of global solutions of the problem. Second, for small initial data, we establish the exponential stability of the system by using the energy method. Additionally, we show that if the initial energy assumes a negative value, the solution blows up in finite time.

References

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