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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Zhang, Q. (2017). On the lack of exponential stability for an elastic–viscoelastic waves interaction system. Nonlinear Analysis: Real World Applications, 37, 387-411. https://doi.org/10.1016/j.nonrwa.2017.02.019

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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.

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KW - Gaussian beams

KW - Interaction system

KW - Viscoelastic wave

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

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Keywords

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