Lanzhi Cao, Sheng-Jie Li, Shugen Chai
Abstract:
In this article, we investigate the exponential stabilization of a
degenerate Euler-Bernoulli beam on an elastic foundation with axial force.
The control input at the boundary features a fractional derivative-type
delay. We construct a tailored Lyapunov functional, specifically designed
to offset the effects of time delay and capture the intrinsic internal
dynamics of the degenerate beam, thereby rigorously establishing the
exponential stability of the system.
Submitted February 12, 2026. Published September 22, 2026.
Math Subject Classifications: P58J35, 53E20.
Key Words: Degenerate beam equation; elastic foundation; axial force; fractional derivative;
time delay; Lyapunov functional.
DOI: 10.58997/ejde.2026.73
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| Lanzhi Cao School of Mathematics and Statistics Shanxi University Taiyuan 030006, China email: caolanzhi1114@163.com |
| Sheng-Jie Li School of Mathematical Sciences Fudan University Shanghai 200433, China email: lishengjiebo@163.com, li_sj@fudan.edu.cn |
| Shugen Chai School of Mathematics and Statistics Shanxi University Taiyuan, 030006, China email: sgchai@sxu.edu.cn |
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