An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound

Rogelio Arancibia; Rodrigo Lecaros; Alberto Mercado; Sebastián Zamorano

An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound

Analysis of PDEs 2021-11-08 v4

Authors: Rogelio Arancibia , Rodrigo Lecaros , Alberto Mercado , Sebastián Zamorano

Abstract

In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz stability for this inverse problem, and we design a convergent algorithm for the reconstruction of the unknown coefficient. The techniques used are based on Carleman inequalities for wave equations and properties of the MGT equation.

Keywords

inverse problem Moore-Gibson-Thompson equation high intensity ultrasound Lipschitz stability Carleman inequalities

Cite

@article{arxiv.2001.07673,
  title  = {An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound},
  author = {Rogelio Arancibia and Rodrigo Lecaros and Alberto Mercado and Sebastián Zamorano},
  journal= {arXiv preprint arXiv:2001.07673},
  year   = {2021}
}

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