Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators

Jerry Bartolomeo; Irena Lasiecka; Roberto Triggiani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1989)

  • Volume: 83, Issue: 1, page 121-128
  • ISSN: 0392-7881

Abstract

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We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.

How to cite

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Bartolomeo, Jerry, Lasiecka, Irena, and Triggiani, Roberto. "Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 83.1 (1989): 121-128. <http://eudml.org/doc/289326>.

@article{Bartolomeo1989,
abstract = {We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.},
author = {Bartolomeo, Jerry, Lasiecka, Irena, Triggiani, Roberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Euler-Bernoulli equations; Uniform stabilization},
language = {eng},
month = {12},
number = {1},
pages = {121-128},
publisher = {Accademia Nazionale dei Lincei},
title = {Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators},
url = {http://eudml.org/doc/289326},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Bartolomeo, Jerry
AU - Lasiecka, Irena
AU - Triggiani, Roberto
TI - Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 121
EP - 128
AB - We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.
LA - eng
KW - Euler-Bernoulli equations; Uniform stabilization
UR - http://eudml.org/doc/289326
ER -

References

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  2. 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
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  6. LAGNESE, J., 1988. Paper presented at International Workshop held in Vorau. Austria, July 10-16. 
  7. LAGNESE, J., 1989. Boundary stabilization of thin elastic plates, SIAM Studies in Applied Mathem. MR1061153DOI10.1137/1.9781611970821
  8. 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. 
  9. LAGNESE, J., A note on boundary stabilization of wave equations. SIAM J. Control, to appear. Zbl0657.93052MR957663DOI10.1137/0326068
  10. 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
  11. LIONS, J.L., 1988. Exact controllability, stabilization and perturbations. SIAM Review, March 1988, to appear in extended version by Masson. 
  12. LIONS, J.L., 1986. Un résultat de régularité (paper dedicated to S. Mizohata), Current Topics on Partial Differential Equations, Kinokuniya Company, Tokyo. 
  13. LAGNESE, J. - LIONS, J.L., 1988. Modelling, analysis and control of thin plates. Masson. Zbl0662.73039MR953313
  14. LASIECKA, I. - TRIGGIANI, R., 1987. Exact controllability of the Euler-Bernoulli equation with L 2 ( Σ ) -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
  15. 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
  16. 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. 
  17. LASIECKA, I. - TRIGGIANI, R., 1987. Uniform exponential energy decay of the wave equation in a bounded region with L 2 ( 0 , ; L 2 ( Γ ) -feedback control in the Dirichlet boundary conditions. J. Diff. Eqs., 66: 340-390. Zbl0629.93047
  18. 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
  19. 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
  20. 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. 
  21. 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). 
  22. 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

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