Exponential stabilization of nonuniform Timoshenko beam with locally distributed feedbacks
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Abstract
The stabilization of the Timoshenko equation of a nonuniform beam with locally distributed feedbacks is considered. It is proved that the system is exponentially stabilizable. The frequency domain method and the multiplier technique are applied.
1991 MR Subject Classification
93C20Keywords
Nonuniform beam Timoshenko equation C0-semigroup locally distribulted feedback exponential stability multiplierPreview
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References
- 1.Kim, J. U., Renardy, Y., Boundary control of the Timoshenko beam, SIAM J. Control Optim., 1987, 25:1417–1429.MATHCrossRefMathSciNetGoogle Scholar
- 2.Feng, D. X., Shi, D. H., Zhang, W. T., Boundary feedback stabilization of Timoshenko beam with boundary dissipation, Science in China (Series A), 1998, 41:483–490.MATHCrossRefMathSciNetGoogle Scholar
- 3.Shi, D. H., Hou, S. H., Feng, D. X., Feedback stabilization of a Timoshenko beam with an end mass, Internat J. Control, 1998, 69:285–300.MATHCrossRefMathSciNetGoogle Scholar
- 4.Shi, D. H., Feng, D. X. Exponential stability of Timoshenko beam with locally distributed feedback, preprint.Google Scholar
- 5.Liu, K. and Liu, Z., Boundary stabilization of nonhomogeneous beam by frequency domain multiplier method, prepint.Google Scholar
- 6.Adams, R. A., Sobolev Space, Academic Press, 1975.Google Scholar
- 7.Gearhart, L. M., Spectral theory for contraction semigroups on Hilbert space, Trans. Amer. Math. Soc., 1978, 236:385–394.MATHCrossRefMathSciNetGoogle Scholar
- 8.Huang, F., Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. of Differential Equations, 1985, 1:43–53.MATHGoogle Scholar
- 9.Prüss, J., On the spectrum of C 0-semigroups, Trans. Amer. Math. Soc., 1984, 284:847–857.MATHCrossRefMathSciNetGoogle Scholar
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© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 2000