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^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	387-411
Number of pages	25
Journal	Nonlinear Analysis: Real World Applications
Volume	37
DOIs	https://doi.org/10.1016/j.nonrwa.2017.02.019
Publication status	Published - 1 Oct 2017

Keywords

Exponential stability
Gaussian beams
Interaction system
Viscoelastic wave

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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–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",

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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

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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

Abstract

Keywords

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