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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.
@article{COCV_2002__8__375_0,
author = {Chambolle, Antonin and Santosa, Fadil},
title = {Control of the wave equation by time-dependent coefficient},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {375--392},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002029},
mrnumber = {1932956},
zbl = {1073.35032},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002029/}
}
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 SP - 375 EP - 392 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002029/ DO - 10.1051/cocv:2002029 LA - en ID - COCV_2002__8__375_0 ER -
%0 Journal Article %A Chambolle, Antonin %A Santosa, Fadil %T Control of the wave equation by time-dependent coefficient %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 375-392 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002029/ %R 10.1051/cocv:2002029 %G en %F COCV_2002__8__375_0
Chambolle, Antonin; Santosa, Fadil. Control of the wave equation by time-dependent coefficient. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 375-392. doi: 10.1051/cocv:2002029
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