We study an initial boundary-value problem for a wave equation with time-dependent soundspeed. In the control problem, we wish to determine a soundspeed function which damps the vibration of the system. We consider the case where the soundspeed 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 energy decay. We illustrate the rich behavior of this problem in numerical examples.
Institute for Mathematics and Its Applications>IMA Preprints Series
Chambolle, Antonin; Santosa, Fadil.
Control of the wave equation by time-dependent coefficient.
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