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
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Adama Coulibaly
Université Felix Houphouët-Boigny and
UFR Mathématiques
Appliquées et Informatique
Côte d'Ivoire
email: couliba@yahoo.fr
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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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