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

28 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

Access

10.3934/dcds.2009.23.399

OpenUrl availability

Full text

Cite this

@article{b5758adb78a542aea4aa10f0dc0c280e,

title = "A spectral approach to the indirect boundary control of a system of weakly coupled wave equations",

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",

year = "2009",

month = jan,

doi = "10.3934/dcds.2009.23.399",

language = "English (US)",

volume = "23",

pages = "399--414",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "1-2",

}

TY - JOUR

T1 - A spectral approach to the indirect boundary control of a system of weakly coupled wave equations

AU - Liu, Zhuangyi

AU - Rao, Bopeng

PY - 2009/1

Y1 - 2009/1

N2 - 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.

AB - 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.

KW - Exact controllability

KW - Ingham's inequality

KW - Non harmonic analysis

KW - Weak observability

UR - http://www.scopus.com/inward/record.url?scp=60949111092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60949111092&partnerID=8YFLogxK

U2 - 10.3934/dcds.2009.23.399

DO - 10.3934/dcds.2009.23.399

M3 - Article

AN - SCOPUS:60949111092

SN - 1078-0947

VL - 23

SP - 399

EP - 414

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 1-2

ER -

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

Abstract

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this