Observability and controllability of the 1--d wave equation in domains with moving boundary
Abstract
By mean of generalized Fourier series and Parseval's equality in weighted L2--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp time, at each of the endpoints of the interval. The observability constants are explicitly given. Using the Hilbert Uniqueness Method we deduce the exact boundary controllability of the wave equation.
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