Zhang X, Zheng C, Zuazua E (2009)
Publication Type: Journal article
Publication year: 2009
Book Volume: 23
Pages Range: 571-604
Journal Issue: 1-2
In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable with uniformly bounded cost with respect to the time-step. In this way, the well-known exact-controllability property of the wave equation can be reproduced as the limit, as the time step h -> 0, of the controllability of projections of the time-discrete one. By duality these results are equivalent to deriving uniform observability estimates (with respect to h -> 0) within a class of solutions of the time-discrete problem in which the high frequency components have been filtered. The later is established by means of a time-discrete version of the classical multiplier technique. The optimality of the order of the filtering parameter is also established, although a careful analysis of the expected velocity of propagation of time-discrete waves indicates that its actual value could be improved.
APA:
Zhang, X., Zheng, C., & Zuazua, E. (2009). TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL. Discrete and Continuous Dynamical Systems, 23(1-2), 571-604. https://doi.org/10.3934/dcds.2009.23.571
MLA:
Zhang, Xu, Chuang Zheng, and Enrique Zuazua. "TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL." Discrete and Continuous Dynamical Systems 23.1-2 (2009): 571-604.
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