Eventual differentiability of a string with local Kelvin-Voigt damping

Kangsheng Liu; Zhuangyi Liu; Qiong Zhang

doi:10.1051/cocv/2015055

Eventual differentiability of a string with local Kelvin-Voigt damping

Kangsheng Liu, Zhuangyi Liu, Qiong Zhang

Mathematics & Statistics

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

11 Scopus citations

Abstract

In this paper, we study a wave equation with local Kelvin-Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.

Original language	English (US)
Pages (from-to)	443-454
Number of pages	12
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	23
Issue number	2
DOIs	https://doi.org/10.1051/cocv/2015055
State	Published - Apr 1 2017

Keywords

Eventual differentiability of semigroup
Local Kelvin-Voigt damping
Semigroup

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abstract = "In this paper, we study a wave equation with local Kelvin-Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.",

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AU - Zhang, Qiong

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N2 - In this paper, we study a wave equation with local Kelvin-Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.

AB - In this paper, we study a wave equation with local Kelvin-Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.

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KW - Local Kelvin-Voigt damping

KW - Semigroup

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JF - ESAIM - Control, Optimisation and Calculus of Variations

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