Zhang X, Zheng C, Zuazua E (2010)
Publication Type: Book chapter / Article in edited volumes
Publication year: 2010
Publisher: Springer Netherland
Edited Volumes: Applied and Numerical Partial Differential Equations
Series: Computational Methods in Applied Sciences
Book Volume: 15
Pages Range: 229-245
DOI: 10.1007/978-90-481-3239-3_17
In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space in which the high frequencies have been filtered is exactly controllable with uniformly bounded controls (with respect to the time-step). By classical duality arguments, the problem is reduced to a boundary observability inequality for a time-discrete wave equation. Using multiplier techniques the uniform observability property is proved in a class of filtered initial data. The optimality of the filtering parameter is also analyzed.
APA:
Zhang, X., Zheng, C., & Zuazua, E. (2010). Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach. In W. Fitzgibbon, Y.A. Kuznetsov, Pekka Neittaanmäki, Jacques Périaux, Olivier Pironneau (Eds.), Applied and Numerical Partial Differential Equations. (pp. 229-245). Springer Netherland.
MLA:
Zhang, Xu, Chuang Zheng, and Enrique Zuazua. "Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach." Applied and Numerical Partial Differential Equations. Ed. W. Fitzgibbon, Y.A. Kuznetsov, Pekka Neittaanmäki, Jacques Périaux, Olivier Pironneau, Springer Netherland, 2010. 229-245.
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