Electron. J. Differential Equations, Vol. 2023 (2023), No. 68, pp. 1-18.

Stability and instability of Kirchhoff plate equations with delay on the boundary control

Haidar Badawi, Mohammad Akil, Zayd Hajjej

In this article, we consider the Kirchhoff plate equation with delay terms on the boundary control. We give instability examples of systems for some choices of delays. Finally, we prove its well-posedness, strong stability, and exponential stability under a multiplier geometric control condition.

Submitted April 18, 2023. Published October 16, 2023.
Math Subject Classifications: 74K20, 47D60, 90C31, 93D15, 93D20, 35B35, 35B40, 93C80, 93C43.
Key Words: Kirchhoff plate equation; boundary control; time delay; instability examples; strong stability; exponential stability.
DOI: 10.58997/ejde.2023.68

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Haidar Badawi
PDEs with applications in materials sciences and biology
Department of Mathematics and Physics
Lebanese International University LIU, Beirut, Lebanon
email: haidar.badawi@liu.edu.lb
Mohammad Akil
Univ. Polytechnique Hauts-de-France
INSA Hauts-de-France, CERAMATHS
Laboratoire de Materiaux Ceramiques et de Mathematiques
F-59313 Valenciennes, France
email: mohammad.akil@uphf.fr
Zayd Hajjej
Department of Mathematics
College of Science
King Saud University
P.O. Box 2455, Riyadh 11451, Saudi Arabia
email: zhajjej@ksu.edu.sa

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