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 Lincei. Matematica e Applicazioni (1989)

  • Volume: 83, Issue: 1, page 121-128
  • ISSN: 1120-6330

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 Lincei. Matematica e Applicazioni 83.1 (1989): 121-128. <http://eudml.org/doc/287328>.

@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 Lincei. Matematica e Applicazioni},
keywords = {Euler-Bernoulli equations; Uniform stabilization; well posedness; 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/287328},
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 Lincei. Matematica e Applicazioni
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; well posedness; uniform stabilization
UR - http://eudml.org/doc/287328
ER -

References

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  1. BARTOLOMEO, J. - TRIGGIANI, R., 1988. Uniform stabilization of the Euler-Bernoulli equation with Dirichlet and Neumann boundary feedback. SIAM J. Mathematical Analysis, to appear. 
  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. Zbl0414.35044MR544253
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  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. Zbl0652.35029MR910523DOI10.1007/BFb0038760
  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. Zbl0644.49028MR963060
  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. Zbl0666.49011MR999836
  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. Zbl0666.49013MR984832DOI10.1137/0327018
  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. Zbl0629.93047MR876804DOI10.1016/0022-0396(87)90025-8
  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). Zbl0686.35067MR920578
  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. Zbl0666.49013MR1179444DOI10.1007/BFb0005156

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