In this paper, we continue our study of the damped Rayleigh beam system. The purpose of this work is to add two additional force controls in moment and rotation and see if this remains exponentially stable. Thus we obtain a four-control system. Using the Riesz basis approach, we prove the stability of nonhomogeneous Rayleigh beam via an indefinite damping and the boundary control feedbacks in position, velocity, moment and rotation. We transform the system to an evolution problem and prove that the linear operator of the Cauchy problem generates a  semigroup of contractions. Subsequently, we show how the damping term can affect the decay rate asymptotically.

beam equation, semigroup theory, asymptotic analysis, Riesz basis, exponential stability.

Received: November 5, 2024; Accepted: December 13, 2024; Published: February 28, 2025

How to cite this article: Kouassi Ayo Ayébié Hermith, Diop Fatou N., Yapi Serge Alain Joresse and Touré K. Augustin, Stability of variable coefficients Rayleigh beams with indefinite damping under a force control, Far East Journal of Dynamical Systems 38(1) (2025), 127-157. https://doi.org/10.17654/0972111825006

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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