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Bartolomeo, Jerry and Lasiecka, Irena and Triggiani, Roberto:
Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators (Decadimento uniforme esponenziale dell'energia nelle equazioni di Euler-Bernoulli con opportuna dissipazione sulla frontiera)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 83 (1989), fasc. n.1, p. 121-128, (English)
pdf (974 Kb), djvu (992 Kb). | MR 1142449 | Zbl 0749.93047

Sunto

Studiamo, al variare delle condizioni al contorno, il problema di stabilizzazione uniforme per l'equazione di Euler-Bernoulli con dissipazione definita su un dominio regolare limitato di dimensione qualunque.
Referenze Bibliografiche
[1] J. BARTOLOMEO - R. TRIGGIANI, 1988. Uniform stabilization of the Euler-Bernoulli equation with Dirichlet and Neumann boundary feedback. SIAM J. Mathematical Analysis, to appear. | MR 2637574 | Zbl 0753.35037
[2] G. CHEN, 1979. Energy decay estimates and exact controllability of the wave equation in a bounded domain. J. Math. Pures et Appl., (9), 58: 249-274. | MR 544253
[3] G. CHEN, 1981. A note on the boundary stabilization of the wave equation. SIAM J. Control, 19: 106-113. | fulltext (doi) | MR 603083 | Zbl 0461.93036
[4] F. FLANDOLI - I. LASIECKA - R. TRIGGIANI, Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli equations. Annali di Matematica Pura e Applicata, to appear. | Zbl 0674.49004
[5] J.V. KIM - Y. RANARDY, 1987. Boundary control of the Timoshenkso beam. SIAM J. Control, 25: 1147- 1429. | fulltext (doi) | MR 912448
[6] J. LAGNESE, 1988. Paper presented at International Workshop held in Vorau. Austria, July 10-16.
[7] J. LAGNESE, 1989. Boundary stabilization of thin elastic plates, SIAM Studies in Applied Mathem. | fulltext (doi) | MR 1061153
[8] J. LAGNESE, 1987. Uniform boundary stabilization of homogeneous, isotropic plates. Lectures Notes in Control Science, 102, Springer-Verlag: 204-215; Proceedings of the 1986 Vorau Conference on Distributed Parameter Systems.
[9] J. LAGNESE, A note on boundary stabilization of wave equations. SIAM J. Control, to appear. | fulltext (doi) | MR 957663 | Zbl 0657.93052
[10] J. LAGNESE, 1983. Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Diff. Eqts., 50, (2): 163-182. | fulltext (doi) | MR 719445 | Zbl 0536.35043
[11] J.L. LIONS, 1988. Exact controllability, stabilization and perturbations. SIAM Review, March 1988, to appear in extended version by Masson.
[12] J.L. LIONS, 1986. Un résultat de régularité (paper dedicated to S. Mizohata), Current Topics on Partial Differential Equations, Kinokuniya Company, Tokyo.
[13] J. LAGNESE - J.L. LIONS, 1988. Modelling, analysis and control of thin plates. Masson. | MR 953313 | Zbl 0662.73039
[14] I. LASIECKA - R. TRIGGIANI, 1987. Exact controllability of the Euler-Bernoulli equation with $L^{2}(\Sigma)$-control only in the Dirichlet boundary conditions. Atti della Accademia Nazionale dei Lincei, Rendiconti Classe di Scienze fisiche, matematiche e naturali, vol. 81, Roma. | fulltext EuDML | Zbl 0666.49011
[15] I. LASIECKA - R. TRIGGIANI, 1989. Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions: a non-conservative case. SIAM J. Control & Optimization, 27: 330-373. | Zbl 0666.49013
[16] I. LASIECKA - R. TRIGGIANI, 1987. A direct approach to exact controllability for the wave equation with Neumann boundary control and to an Euler-Bernoulli equation. Proceedings 26th IEEE Conference, 529-534, Los Angeles.
[17] I. LASIECKA - R. TRIGGIANI, 1987. Uniform exponential energy decay of the wave equation in a bounded region with $L_{2} (0,\infty; L_{2}(\Gamma)$-feedback control in the Dirichlet boundary conditions. J. Diff. Eqs., 66: 340-390. | Zbl 0629.93047
[18] I. LASIECKA - R. TRIGGIANI, 1988. Regularity theory for a class of non-homogeneous Euler Bernoulli equations: a cosine operator approach. Bollettino Unione Matematica Italiana, (7), 3-B (1989): 199-228. | MR 997339 | Zbl 0685.35029
[19] I. LASIECKA - R. TRIGGIANI, 1990. Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement and moments. J. Mathem. Analysis & Applic., 146: 1-33. | fulltext (doi) | MR 1041199 | Zbl 0694.49026
[20] I. LASIECKA - R. TRIGGIANI, 1989. Uniform exponential energy decay of the Euler-Bernoulli equation on a bounded region with boundary feedback acting on the bending moment. Dept. of Applied Mathem. Report, University of Virginia.
[21] R. TRIGGIANI, 1987. Wave equation on a bounded domain with boundary dissipation: an operator approach. J. Mathem. Anal. & Applic., 37 (1989), 438-461; Operator Methods for Optimal Control Problems, Lectures Notes in Pure and Applied Mathematics, 108: 283-310 (LEE Ed.), Marcel Dekker; also in Recent Advances in Communication and Control Theory, honoring the sixtieth anniversary of A.V. Balakrishnan (R.E. KALMAN and G.I. MARCHUK, Eds.), 262-286, Optimization Software (New York, 1987).
[22] I. LASIECKA - R. TRIGGIANI, 1989. Further results on exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions, to appear. | fulltext (doi) | MR 984832 | Zbl 0666.49013

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