An inverse problem for Moore–Gibson–Thompson equation arising in high intensity ultrasound-Reference-Cited by-同舟云学术

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

Published:2022-04-28 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Arancibia Rogelio¹,Lecaros Rodrigo¹^ORCID,Mercado Alberto¹,Zamorano Sebastián²^ORCID

Affiliation:

1. Departamento de Matemática , Universidad Técnica Federico Santa María , Casilla 110-V , Valparaíso , Chile

2. Departamento de Matemática y Ciencia de la Computación , Facultad de Ciencia , Universidad de Santiago de Chile (USACH) , Casilla 307, Correo 2 , Santiago , Chile

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0090/pdf

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