# On the nonlinear stabilization of the wave equation

Annales Polonici Mathematici (1998)

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

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topAissa 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

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- [3] A. Guesmia, Stabilisation frontière non linéaire d'un système isotropique d'élasticité, submitted.
- [4] V. Komornik, Exact Controllability and Stabilization, the Multiplier Method, Masson-Wiley, Paris, 1994.
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- [6] V. Komornik, On the nonlinear boundary stabilization of the wave equation, Chinese Ann. Math. Ser. B 14 (1993), 153-164. Zbl0804.35065
- [7] V. Komornik, Rapid boundary stabilization of the wave equation, SIAM J. Control Optim. 29 (1991), 197-208. Zbl0749.35018
- [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] 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] M. Nakao, Energy decay for the wave equation with a nonlinear weak dissipation, Differential Integral Equations 8 (1995), 681-688. Zbl0848.35076
- [11] E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback, SIAM J. Control Optim. 28 (1990), 446-477. Zbl0695.93090

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