# Control of the Wave Equation by Time-Dependent Coefficient

Antonin Chambolle; Fadil Santosa

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 375-392. <http://eudml.org/doc/90653>.

@article{Chambolle2010,

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.; damping; energy decay},

language = {eng},

month = {3},

pages = {375-392},

publisher = {EDP Sciences},

title = {Control of the Wave Equation by Time-Dependent Coefficient},

url = {http://eudml.org/doc/90653},

volume = {8},

year = {2010},

}

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

DA - 2010/3//

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.; damping; energy decay

UR - http://eudml.org/doc/90653

ER -

## References

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- J. Restorff, Magnetostrictive materials and devices, in Encyclopedia of Applied Physics, Vol. 9. VCH Publishers (1994).

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