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2019 Well-posedness and stability for a viscoelastic wave equation with density and time-varying delay in $\mathbb {R}^n$
Baowei Feng, Xinguang Yang, Keqin Su
J. Integral Equations Applications 31(4): 465-493 (2019). DOI: 10.1216/JIE-2019-31-4-465

Abstract

This paper concerns the well-posedness and energy decay of a linear wave equation with density, infinite memory and time-varying delay in the whole space $\mathbb {R}^n$ $(n\geq 3)$. We consider the weighted spaces $\mathcal {D}^{1,2}(\mathbb {R}^n)$ and $L^2_{\rho }(\mathbb {R}^n)$ introduced by Karachalios and Stavrakakis (1999) to overcome the difficulty that some operators on $\mathbb {R}^n$ are not compact. We prove the global well-posedness of the Cauchy problem by using Faedo-Galerkin approximation and establish the exponential decay of energy when the amplitude of the time delay term is small by using suitable Lyapunov functional.

Citation

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Baowei Feng. Xinguang Yang. Keqin Su. "Well-posedness and stability for a viscoelastic wave equation with density and time-varying delay in $\mathbb {R}^n$." J. Integral Equations Applications 31 (4) 465 - 493, 2019. https://doi.org/10.1216/JIE-2019-31-4-465

Information

Published: 2019
First available in Project Euclid: 6 February 2020

zbMATH: 07169457
MathSciNet: MR4060436
Digital Object Identifier: 10.1216/JIE-2019-31-4-465

Subjects:
Primary: 35B40
Secondary: 35L05 , 74Dxx , 93D15 , 93D20

Keywords: Delay , Density , memory , wave equation , ‎weighted space

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 4 • 2019
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