On the exponential decay of a Balakrishnan-Taylor plate with strong damping

Zayd Hajjej; Zayd Hajjej

doi:10.3934/math.2024682

AIMS Mathematics

2024, Volume 9, Issue 6: 14026-14042. doi: 10.3934/math.2024682

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Research article

On the exponential decay of a Balakrishnan-Taylor plate with strong damping

Zayd Hajjej ^,

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

Received: 03 January 2024 Revised: 30 March 2024 Accepted: 08 April 2024 Published: 18 April 2024
MSC : 35B40, 35L75, 74K10

In this manuscript, we study a thin and narrow plate equation that models the deck of a suspension bridge that is subject to a Balakrishnan-Taylor damping and a strong damping. First, by using the Faedo Galerkin method, we prove the existence of both global weak and regular solutions. Second, we prove the exponential stability of the energy for regular solutions by combining the multiplier method and a well-known result of Komornik.
- plate,
- Balakrishnan-Taylor damping,
- strong damping,
- exponential decay
Citation: Zayd Hajjej. On the exponential decay of a Balakrishnan-Taylor plate with strong damping[J]. AIMS Mathematics, 2024, 9(6): 14026-14042. doi: 10.3934/math.2024682

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Abstract

In this manuscript, we study a thin and narrow plate equation that models the deck of a suspension bridge that is subject to a Balakrishnan-Taylor damping and a strong damping. First, by using the Faedo Galerkin method, we prove the existence of both global weak and regular solutions. Second, we prove the exponential stability of the energy for regular solutions by combining the multiplier method and a well-known result of Komornik.

References

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