On the nonlinear stabilization of the wave equation

Aissa Guesmia

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 2, page 191-198
  • ISSN: 0066-2216

Abstract

top
We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

How to cite

top

Aissa Guesmia. "On the nonlinear stabilization of the wave equation." Annales Polonici Mathematici 68.2 (1998): 191-198. <http://eudml.org/doc/270562>.

@article{AissaGuesmia1998,
abstract = {We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.},
author = {Aissa Guesmia},
journal = {Annales Polonici Mathematici},
keywords = {wave equation; nonlinear damping; integral inequality; wave equation with damping; exponential energy decay},
language = {eng},
number = {2},
pages = {191-198},
title = {On the nonlinear stabilization of the wave equation},
url = {http://eudml.org/doc/270562},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Aissa Guesmia
TI - On the nonlinear stabilization of the wave equation
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 2
SP - 191
EP - 198
AB - We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
LA - eng
KW - wave equation; nonlinear damping; integral inequality; wave equation with damping; exponential energy decay
UR - http://eudml.org/doc/270562
ER -

References

top
  1. [1] J. B. Ball, On the asymptotic behavior of generalized processes with applications to nonlinear evolution equations, J. Differential Equations 27 (1978), 224-265. Zbl0376.35002
  2. [2] F. Conrad and M. Pierre, Stabilization of second order evolution equations by unbounded nonlinear feedback, Ann. Inst. Henri Poincaré 11 (1994), 485-515. Zbl0841.93028
  3. [3] A. Guesmia, Stabilisation frontière non linéaire d'un système isotropique d'élasticité, submitted. 
  4. [4] V. Komornik, Exact Controllability and Stabilization, the Multiplier Method, Masson-Wiley, Paris, 1994. 
  5. [5] V. Komornik, Decay estimates for the wave equation with internal damping, in: Proc. Conf. Control Theory, Vorau 1993, Internat. Ser. Numer Anal. 118, Birkhäuser, Basel, 1994, 253-266. Zbl0810.35064
  6. [6] V. Komornik, On the nonlinear boundary stabilization of the wave equation, Chinese Ann. Math. Ser. B 14 (1993), 153-164. Zbl0804.35065
  7. [7] V. Komornik, Rapid boundary stabilization of the wave equation, SIAM J. Control Optim. 29 (1991), 197-208. Zbl0749.35018
  8. [8] V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. 69 (1990), 33-54. Zbl0636.93064
  9. [9] M. Nakao, On the decay of solutions of some nonlinear dissipative wave equations in higher dimensions, Math. Z. 193 (1986), 227-234. Zbl0658.35064
  10. [10] M. Nakao, Energy decay for the wave equation with a nonlinear weak dissipation, Differential Integral Equations 8 (1995), 681-688. Zbl0848.35076
  11. [11] E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback, SIAM J. Control Optim. 28 (1990), 446-477. Zbl0695.93090

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.