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arXiv · 2301.07847

Stability for Time-domain Elastic Wave Equations

Bochao Chen·Yixian Gao·Shuguan Ji·Yang Liu
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Abstract

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the Dirichlet-to-Neumann operator. The reconstruction is mainly based on the modified boundary control method and complex geometric optics solutions for the elastic wave. Next, the stable observability is obtained by a Carleman estimate. Finally, the stability for the density is presented by the connect operator.

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Bochao Chen, Yixian Gao, Shuguan Ji, Yang Liu. 2023-01-19. Stability for Time-domain Elastic Wave Equations. https://arxiv.org/abs/2301.07847

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