Electron. J. Diff. Equ., Vol. 2015 (2015), No. 54, pp. 1-20.

Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity

K. Augustin Toure, Adama Coulibaly, Ayo A. Hermith Kouassi

Abstract:
This article concerns the Riesz basis property and the stability of a damped Euler-Bernoulli beam with nonuniform thickness or density, that is clamped at one end and is free at the other. To stabilize the system, we apply a linear boundary control force in position and velocity at the free end of the beam. We first put some basic properties for the closed-loop system and then analyze the spectrum of the system. Using the modern spectral analysis approach for two-points parameterized ordinary differential operators, we obtain the Riesz basis property. The spectrum-determined growth condition and the exponential stability are also concluded.

Submitted January 23, 2015. Published February 26, 2015.
Math Subject Classifications: 93C20, 93D15, 35B35, 35P10.
Key Words: Beam equation; asymptotic analysis; Riesz basis; exponential stability.

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K. Augustin Touré
Institut National Polytechnique Houphouët-Boigny de Yamoussoukro
BP 2444 Yamoussoukro, Côte d'Ivoire
email: latourci@yahoo.fr
Adama Coulibaly
Université Felix Houphouët-Boigny and
UFR Mathématiques Appliquées et Informatique
Côte d'Ivoire
email: couliba@yahoo.fr
Ayo A. Hermith Kouassi
Université Felix Houphouët-Boigny and
UFR Mathématiques Appliquées et Informatique
Côte d'Ivoire
email: hermithkouassi@gmail.com

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