Stability for Time-domain Elastic Wave Equations

Bochao Chen; Yixian Gao; Shuguan Ji; Yang Liu

Stability for Time-domain Elastic Wave Equations

Analysis of PDEs 2023-01-20 v1

Authors: Bochao Chen , Yixian Gao , Shuguan Ji , Yang Liu

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.

Keywords

inverse problems inverse scattering solitary waves

Cite

@article{arxiv.2301.07847,
  title  = {Stability for Time-domain Elastic Wave Equations},
  author = {Bochao Chen and Yixian Gao and Shuguan Ji and Yang Liu},
  journal= {arXiv preprint arXiv:2301.07847},
  year   = {2023}
}

Comments

23pp

Related papers

View all related →