Stability of a string with local Kelvin-Voigt damping and nonsmooth coefficient at interface

Zhuangyi Liu; Qiong Zhang

doi:10.1137/15M1049385

Stability of a string with local Kelvin-Voigt damping and nonsmooth coefficient at interface

Zhuangyi Liu, Qiong Zhang

Mathematics & Statistics

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Abstract

In this paper, we study the stability of an elastic string system with local Kelvin Voigt damping. Few results for this system are known in the literature. Under the assumption that the damping coefficient has a singularity at the interface of the damped and undamped regions and behaves like xα near the interface, we prove that the semigroup corresponding to the system is polynomially or exponentially stable and the decay rate depends on the parameter α ∈ (0, 1].

Original language	English (US)
Pages (from-to)	1859-1871
Number of pages	13
Journal	SIAM Journal on Control and Optimization
Volume	54
Issue number	4
DOIs	https://doi.org/10.1137/15M1049385
State	Published - 2016

Bibliographical note

Publisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

Keywords

C semigroup
Exponential stability
Kelvin-Voigt damping
Polynomial stability

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AB - In this paper, we study the stability of an elastic string system with local Kelvin Voigt damping. Few results for this system are known in the literature. Under the assumption that the damping coefficient has a singularity at the interface of the damped and undamped regions and behaves like xα near the interface, we prove that the semigroup corresponding to the system is polynomially or exponentially stable and the decay rate depends on the parameter α ∈ (0, 1].

KW - C semigroup

KW - Exponential stability

KW - Kelvin-Voigt damping

KW - Polynomial stability

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Stability of a string with local Kelvin-Voigt damping and nonsmooth coefficient at interface

Abstract

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