# Control of the wave equation by time-dependent coefficient

Antonin Chambolle; Fadil Santosa

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 375-392
- ISSN: 1292-8119

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topChambolle, Antonin, and Santosa, Fadil. "Control of the wave equation by time-dependent coefficient." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 375-392. <http://eudml.org/doc/244640>.

@article{Chambolle2002,

abstract = {We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of this problem in numerical examples.},

author = {Chambolle, Antonin, Santosa, Fadil},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {control problem; time dependent wave equation; damping; energy decay},

language = {eng},

pages = {375-392},

publisher = {EDP-Sciences},

title = {Control of the wave equation by time-dependent coefficient},

url = {http://eudml.org/doc/244640},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Chambolle, Antonin

AU - Santosa, Fadil

TI - Control of the wave equation by time-dependent coefficient

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 375

EP - 392

AB - We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of this problem in numerical examples.

LA - eng

KW - control problem; time dependent wave equation; damping; energy decay

UR - http://eudml.org/doc/244640

ER -

## References

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- [6] S. Pohozaev, On a class of quasilinear hyperbolic equations. Math. USSR Sbornik 25 (1975) 145-158. Zbl0328.35060
- [7] J. Restorff, Magnetostrictive materials and devices, in Encyclopedia of Applied Physics, Vol. 9. VCH Publishers (1994).

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