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Increasing stability for the inverse source problem in elastic waves with attenuation

Part of: Miscellaneous topics - Partial differential equations Optics, electromagnetic theory - General

Published online by Cambridge University Press:  20 April 2023

Ganghua Yuan  and
Yue Zhao
Ganghua Yuan
Affiliation:
KLAS, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, China
Yue Zhao*
Affiliation:
School of Mathematics and Statistics, and Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University, Wuhan 430079, China
*
*Correspondence author. Email: zhaoyueccnu@163.com
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Abstract

This paper is concerned with the increasing stability of the inverse source problem for the elastic wave equation with attenuation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases. The stability also shows exponential dependence on the attenuation coefficient. The ingredients of the analysis include Carleman estimates and time decay estimates for the elastic wave equation to obtain an exact observability bound, and the study of the resonance-free region and an upper bound of the resolvent in this region for the elliptic operator with respect to the complex frequency. The advantage of the method developed in this work is that it can be used to study the case of variable attenuation coefficient.

Keywords

Inverse scattering problemelastic waves with attenuationincreasing stability

MSC classification

Primary: 35R30: Inverse problems
Secondary: 78A46: Inverse scattering problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 34 , Issue 4 , August 2023 , pp. 896 - 910
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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