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arXiv · 2510.25484

Exponential Stability of a Degenerate Euler-Bernoulli Beam with Axial Force and Delayed Boundary Control

Ben Bakary Junior Siriki·Adama Coulibaly
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Abstract

This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an appropriate energy space in weighted Sobolev settings. Using Lümer-Phillips theorem, we prove that the linear operator associated with the problem generates a $\mathcal{C}_0$-semigroup of contractions. Next, we establish the uniform exponential stability of the system. By constructing a novel Lyapunov functional incorporating weighted integral terms, we demonstrate that the energy of the system exponentially decays to zero and derive a precise decay rate estimate. This work provides a significant extension to the stability theory for complex distributed parameter systems.

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Ben Bakary Junior Siriki, Adama Coulibaly. 2026-02-20. Exponential Stability of a Degenerate Euler-Bernoulli Beam with Axial Force and Delayed Boundary Control. https://arxiv.org/abs/2510.25484

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