On the lack of exponential stability for an elastic–viscoelastic waves interaction system

Qiong Zhang

doi:10.1016/j.nonrwa.2017.02.019

On the lack of exponential stability for an elastic–viscoelastic waves interaction system

Qiong Zhang^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

13 引用（Scopus）

摘要

In this paper, we consider an interaction system in which a wave and a viscoelastic wave equation evolve in two bounded domains, with natural transmission conditions at a common interface. We show the lack of uniform decay of solutions in general domains. The method is based on the construction of ray-like solutions by means of geometric optics expansions and a careful analysis of the transfer of the energy at the interface.

源语言	英语
页（从-至）	387-411
页数	25
期刊	Nonlinear Analysis: Real World Applications
卷	37
DOI	https://doi.org/10.1016/j.nonrwa.2017.02.019
出版状态	已出版 - 1 10月 2017

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10.1016/j.nonrwa.2017.02.019

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title = "On the lack of exponential stability for an elastic{\textendash}viscoelastic waves interaction system",

abstract = "In this paper, we consider an interaction system in which a wave and a viscoelastic wave equation evolve in two bounded domains, with natural transmission conditions at a common interface. We show the lack of uniform decay of solutions in general domains. The method is based on the construction of ray-like solutions by means of geometric optics expansions and a careful analysis of the transfer of the energy at the interface.",

keywords = "Exponential stability, Gaussian beams, Interaction system, Viscoelastic wave",

author = "Qiong Zhang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Ltd",

year = "2017",

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doi = "10.1016/j.nonrwa.2017.02.019",

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AU - Zhang, Qiong

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N2 - In this paper, we consider an interaction system in which a wave and a viscoelastic wave equation evolve in two bounded domains, with natural transmission conditions at a common interface. We show the lack of uniform decay of solutions in general domains. The method is based on the construction of ray-like solutions by means of geometric optics expansions and a careful analysis of the transfer of the energy at the interface.

AB - In this paper, we consider an interaction system in which a wave and a viscoelastic wave equation evolve in two bounded domains, with natural transmission conditions at a common interface. We show the lack of uniform decay of solutions in general domains. The method is based on the construction of ray-like solutions by means of geometric optics expansions and a careful analysis of the transfer of the energy at the interface.

KW - Exponential stability

KW - Gaussian beams

KW - Interaction system

KW - Viscoelastic wave

UR - https://www.scopus.com/pages/publications/85016160774

U2 - 10.1016/j.nonrwa.2017.02.019

DO - 10.1016/j.nonrwa.2017.02.019

M3 - Article

AN - SCOPUS:85016160774

SN - 1468-1218

VL - 37

SP - 387

EP - 411

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

ER -

On the lack of exponential stability for an elastic–viscoelastic waves interaction system

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