On the observability of time-discrete conservative linear systems
Ervedoza S, Zheng C, Zuazua E (2008)
Publication Type: Journal article
Publication year: 2008
Journal
Book Volume: 254
Pages Range: 3037-3078
Journal Issue: 12
DOI: 10.1016/j.jfa.2008.03.005
Abstract
We consider various time discretization schemes of abstract conservative evolution equations of the form (z) over dot = Az, where A is a skew-adjoint operator. We analyze the problem of observability through an operator B. More precisely, we assume that the pair (A, B) is exactly observable for the continuous model, and we derive uniform observability inequalities for suitable time-discretization schemes within the class of conveniently filtered initial data. The method we use is mainly based on the resolvent estimate given by Burq and Zworski in [N. Burq, M. Zworski, Geometric control in the presence of a black box, J. Amer. Math. Soc. 17(2) (2004) 443-471 (electronic)]. We present some applications of our results to time-discrete schemes for wave, Schrodinger and KdV equations and fully discrete approximation schemes for wave equations. (C) 2008 Elsevier Inc. All rights reserved.
Authors with CRIS profile
Involved external institutions
Versailles Saint-Quentin-en-Yvelines University / Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)
France (FR)
Southwestern University of Finance and Economics (SWUFE) / 西南财经大学
China (CN)
Universidad Autónoma de Madrid (UAM)
Spain (ES)
France (FR)
Southwestern University of Finance and Economics (SWUFE) / 西南财经大学
China (CN)
Universidad Autónoma de Madrid (UAM)
Spain (ES)
How to cite
APA:
Ervedoza, S., Zheng, C., & Zuazua, E. (2008). On the observability of time-discrete conservative linear systems. Journal of Functional Analysis, 254(12), 3037-3078. https://dx.doi.org/10.1016/j.jfa.2008.03.005
MLA:
Ervedoza, Sylvain, Chuang Zheng, and Enrique Zuazua. "On the observability of time-discrete conservative linear systems." Journal of Functional Analysis 254.12 (2008): 3037-3078.
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