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

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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

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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.

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KW - Frequency approach

KW - Graph

KW - Kelvin–Voigt damping

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

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