A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

Zhuangyi Liu; Bopeng Rao

doi:10.3934/dcds.2009.23.399

A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

Zhuangyi Liu, Bopeng Rao

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

In this paper, we study the exact controllability of a system of two weakly coupled one-dimensional wave equations with the control acted on only one equation. Using the non harmonic analysis, we establish the weak observability inequalities, which depend on the ratio of the wave propagation speeds. The obtained results are optimal.

Original language	English (US)
Pages (from-to)	399-414
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	23
Issue number	1-2
DOIs	https://doi.org/10.3934/dcds.2009.23.399
State	Published - Jan 2009

Keywords

Exact controllability
Ingham's inequality
Non harmonic analysis
Weak observability

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10.3934/dcds.2009.23.399

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abstract = "In this paper, we study the exact controllability of a system of two weakly coupled one-dimensional wave equations with the control acted on only one equation. Using the non harmonic analysis, we establish the weak observability inequalities, which depend on the ratio of the wave propagation speeds. The obtained results are optimal.",

keywords = "Exact controllability, Ingham's inequality, Non harmonic analysis, Weak observability",

author = "Zhuangyi Liu and Bopeng Rao",

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KW - Ingham's inequality

KW - Non harmonic analysis

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A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

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