Riesz basis generation and boundary stabilization of two strings connected by a point mass with variable coefficients |
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Authors: | Jamel Ben Amara Walid Boughamda |
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Institution: | Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis el Manar, Mathematical Engineering Laboratory, Tunis, Tunisia |
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Abstract: | In this paper, we study the Riesz basis property and the problem of stabilization of two vibrating strings connected by a point mass with variable physical coefficients under a boundary feedback control acts at one extreme point and Dirichlet boundary condition on the other end. It is shown that the system has a sequence of generalized eigenfunctions which forms a Riesz basis for the state Hilbert space. By a detailed spectral analysis, it is proved that this hybrid system is asymptotically stable but not exponentially stable. |
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Keywords: | asymptotic stability point mass Riesz basis string equation variable coefficients |
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