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Riesz basis approach to the stabilization of a nonuniform Scole model

My Driss Aouragh, Naji Yebari


In this paper, we consider the uniform stabilization of the well known Scole model with variable coefficients in the case of a clamped beam. We prove that the closed loop system is dissipative. By asymptotic analysis of frequencies of the closed loop system, we give asymptotic expressions of the higher frequencies and we show that a sequence of generalized eigenfunctions of the nonuniform Scole model under boundary feedbacks control forms a Riesz basis for the state Hilbert space. Numerical results are also presented. This paper is a non uniform version of the results 3 in the case of a clamped beam.


Beams, linear elasticity, variable coefficients, asymptotic analysis, Riesz Stabilization

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