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Control of the Wave Equation by Time-Dependent Coefficient

Published online by Cambridge University Press:  15 August 2002

Antonin Chambolle  and
Fadil Santosa
Antonin Chambolle
Affiliation:
CEREMADE, UMR 7534 du CNRS, Université de Paris-Dauphine, 75775 Paris Cedex 16, France; antonin.chambolle@ceremade.dauphine.fr.
Fadil Santosa
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.; santosa@math.umn.edu.
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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.

Keywords

Control problemtime dependent wave equationdamping.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 375 - 392
Copyright
© EDP Sciences, SMAI, 2002

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