TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL
Zhang X, Zheng C, Zuazua E (2009)
Publication Type: Journal article
Publication year: 2009
Journal
Book Volume: 23
Pages Range: 571-604
Journal Issue: 1-2
Abstract
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.
Authors with CRIS profile
Involved external institutions
Chinese Academy of Sciences (CAS) / 中国科学院
China (CN)
Beijing Normal University
China (CN)
Basque Center of Applied Mathematics (BCAM)
Spain (ES)
China (CN)
Beijing Normal University
China (CN)
Basque Center of Applied Mathematics (BCAM)
Spain (ES)
How to cite
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://dx.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.
BibTeX: Download