Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach

Zhang X, Zheng C, Zuazua E (2010)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2010

Journal

Computational Vision and Medical Image Processing Springer Science Business Media

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

Abstract

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Beijing Normal University CN China (CN) Chinese Academy of Sciences (CAS) / 中国科学院 CN China (CN) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

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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