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Observability and Controllability of the 1-D Wave Equation in Domains with Moving Boundary

Observability and Controllability of the 1-D Wave Equation in Domains with Moving Boundary By mean of generalized Fourier series and Parseval’s equality in weighted L 2 $L^{2}$ -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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Observability and Controllability of the 1-D Wave Equation in Domains with Moving Boundary

Acta Applicandae Mathematicae , Volume 157 (1) – Feb 27, 2018

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-018-0166-1
Publisher site
See Article on Publisher Site

Abstract

By mean of generalized Fourier series and Parseval’s equality in weighted L 2 $L^{2}$ -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.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Feb 27, 2018

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