Stability of a Graph of Strings with Local Kelvin–Voigt Damping

Kaïs Ammari; Zhuangyi Liu; Farhat Shel

doi:10.1007/978-3-031-14268-0_6

Stability of a Graph of Strings with Local Kelvin–Voigt Damping

Kaïs Ammari
, Zhuangyi Liu
, Farhat Shel

Mathematics & Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under appropriate conditions on the damping coefficients at the vertices, exponential/polynomial stability are proved. This is a new representation of Ammari et al. (Semigroup Forum 100:364–382, 2020), where we considered a tree. Then as indicated in paragraph four of Ammari et al. (Semigroup Forum 100:364–382, 2020), we obtain (under more generalized conditions on the damping coefficients) the same results.

Original language	English (US)
Title of host publication	Tutorials, Schools, and Workshops in the Mathematical Sciences
Publisher	Birkhauser
Pages	169-186
Number of pages	18
DOIs	https://doi.org/10.1007/978-3-031-14268-0_6
State	Published - 2022

Publication series

Name	Tutorials, Schools, and Workshops in the Mathematical Sciences
ISSN (Print)	2522-0969
ISSN (Electronic)	2522-0977

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Dissipative wave operator
Frequency approach
Graph
Kelvin–Voigt damping

Publisher link

10.1007/978-3-031-14268-0_6

Find It

Find It at U of M Libraries

Cite this

@inbook{54aa319944564a4597ad144472e58716,

title = "Stability of a Graph of Strings with Local Kelvin–Voigt Damping",

abstract = "We study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under appropriate conditions on the damping coefficients at the vertices, exponential/polynomial stability are proved. This is a new representation of Ammari et al. (Semigroup Forum 100:364–382, 2020), where we considered a tree. Then as indicated in paragraph four of Ammari et al. (Semigroup Forum 100:364–382, 2020), we obtain (under more generalized conditions on the damping coefficients) the same results.",

keywords = "Dissipative wave operator, Frequency approach, Graph, Kelvin–Voigt damping",

author = "Ka{\"i}s Ammari and Zhuangyi Liu and Farhat Shel",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2022",

doi = "10.1007/978-3-031-14268-0\_6",

language = "English (US)",

series = "Tutorials, Schools, and Workshops in the Mathematical Sciences",

publisher = "Birkhauser",

pages = "169--186",

booktitle = "Tutorials, Schools, and Workshops in the Mathematical Sciences",

}

TY - CHAP

T1 - Stability of a Graph of Strings with Local Kelvin–Voigt Damping

AU - Ammari, Kaïs

AU - Liu, Zhuangyi

AU - Shel, Farhat

PY - 2022

Y1 - 2022

N2 - We study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under appropriate conditions on the damping coefficients at the vertices, exponential/polynomial stability are proved. This is a new representation of Ammari et al. (Semigroup Forum 100:364–382, 2020), where we considered a tree. Then as indicated in paragraph four of Ammari et al. (Semigroup Forum 100:364–382, 2020), we obtain (under more generalized conditions on the damping coefficients) the same results.

AB - We study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under appropriate conditions on the damping coefficients at the vertices, exponential/polynomial stability are proved. This is a new representation of Ammari et al. (Semigroup Forum 100:364–382, 2020), where we considered a tree. Then as indicated in paragraph four of Ammari et al. (Semigroup Forum 100:364–382, 2020), we obtain (under more generalized conditions on the damping coefficients) the same results.

KW - Dissipative wave operator

KW - Frequency approach

KW - Graph

KW - Kelvin–Voigt damping

UR - https://www.scopus.com/pages/publications/85142095311

UR - https://www.scopus.com/pages/publications/85142095311#tab=citedBy

U2 - 10.1007/978-3-031-14268-0_6

DO - 10.1007/978-3-031-14268-0_6

M3 - Chapter

AN - SCOPUS:85142095311

T3 - Tutorials, Schools, and Workshops in the Mathematical Sciences

SP - 169

EP - 186

BT - Tutorials, Schools, and Workshops in the Mathematical Sciences

PB - Birkhauser

ER -

Stability of a Graph of Strings with Local Kelvin–Voigt Damping

Abstract

Publication series

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this