Geodesic
Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 93C20, 93D15, 35B35, 35P10
Keywords: beam equation, asymptotic analysis, Riesz basis, exponential stability 
@article{EJDE_2015__2015__a0,
     author = {Tour\'e,  K.Augustin and Coulibaly,  Adama and Hermith Kouassi,  Ayo A.},
     title = {Riesz basis and exponential stability for {Euler-Bernoulli} beams with variable coefficients and indefinite damping under a force control in position and velocity},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1310.93073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/}
}
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AU  - Hermith Kouassi,  Ayo A.
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JO  - Electronic journal of differential equations
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%A Touré,  K.Augustin
%A Coulibaly,  Adama
%A Hermith Kouassi,  Ayo A.
%T Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/
%G en
%F EJDE_2015__2015__a0
Touré,  K.Augustin; Coulibaly,  Adama; Hermith Kouassi,  Ayo A. Riesz basis and exponential stability for Euler-Bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a0/