Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators
Jerry Bartolomeo; Irena Lasiecka; Roberto Triggiani
- Volume: 83, Issue: 1, page 121-128
- ISSN: 0392-7881
Access Full Article
topAbstract
topHow to cite
topReferences
top- BARTOLOMEO, J. - TRIGGIANI, R., 1988. Uniform stabilization of the Euler-Bernoulli equation with Dirichlet and Neumann boundary feedback. SIAM J. Mathematical Analysis, to appear. Zbl0753.35037MR2637574
- CHEN, G., 1979. Energy decay estimates and exact controllability of the wave equation in a bounded domain. J. Math. Pures et Appl., (9), 58: 249-274. MR544253
- CHEN, G., 1981. A note on the boundary stabilization of the wave equation. SIAM J. Control, 19: 106-113. Zbl0461.93036MR603083DOI10.1137/0319008
- FLANDOLI, F. - LASIECKA, I. - TRIGGIANI, R., Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli equations. Annali di Matematica Pura e Applicata, to appear. Zbl0674.49004
- KIM, J.V. - RANARDY, Y., 1987. Boundary control of the Timoshenkso beam. SIAM J. Control, 25: 1147- 1429. MR912448DOI10.1137/0325078
- LAGNESE, J., 1988. Paper presented at International Workshop held in Vorau. Austria, July 10-16.
- LAGNESE, J., 1989. Boundary stabilization of thin elastic plates, SIAM Studies in Applied Mathem. MR1061153DOI10.1137/1.9781611970821
- LAGNESE, J., 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.
- LAGNESE, J., A note on boundary stabilization of wave equations. SIAM J. Control, to appear. Zbl0657.93052MR957663DOI10.1137/0326068
- LAGNESE, J., 1983. Decay of solutions of wave equations in a bounded region with boundary dissipation. J. Diff. Eqts., 50, (2): 163-182. Zbl0536.35043MR719445DOI10.1016/0022-0396(83)90073-6
- LIONS, J.L., 1988. Exact controllability, stabilization and perturbations. SIAM Review, March 1988, to appear in extended version by Masson.
- LIONS, J.L., 1986. Un résultat de régularité (paper dedicated to S. Mizohata), Current Topics on Partial Differential Equations, Kinokuniya Company, Tokyo.
- LAGNESE, J. - LIONS, J.L., 1988. Modelling, analysis and control of thin plates. Masson. Zbl0662.73039MR953313
- LASIECKA, I. - TRIGGIANI, R., 1987. Exact controllability of the Euler-Bernoulli equation with -control only in the Dirichlet boundary conditions. Atti della Accademia Nazionale dei Lincei, Rendiconti Classe di Scienze fisiche, matematiche e naturali, vol. 81, Roma. Zbl0666.49011
- LASIECKA, I. - TRIGGIANI, R., 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. Zbl0666.49013
- LASIECKA, I. - TRIGGIANI, R., 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.
- LASIECKA, I. - TRIGGIANI, R., 1987. Uniform exponential energy decay of the wave equation in a bounded region with -feedback control in the Dirichlet boundary conditions. J. Diff. Eqs., 66: 340-390. Zbl0629.93047
- LASIECKA, I. - TRIGGIANI, R., 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. Zbl0685.35029MR997339
- LASIECKA, I. - TRIGGIANI, R., 1990. Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement and moments. J. Mathem. Analysis & Applic., 146: 1-33. Zbl0694.49026MR1041199DOI10.1016/0022-247X(90)90330-I
- LASIECKA, I. - TRIGGIANI, R., 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.
- TRIGGIANI, R., 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).
- LASIECKA, I. - TRIGGIANI, R., 1989. Further results on exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions, to appear. Zbl0666.49013MR984832DOI10.1137/0327018