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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 21, Issue 6


An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement

Shitao Liu / Roberto Triggiani
Published Online: 2013-11-02 | DOI: https://doi.org/10.1515/jip-2012-0096


In this paper, we consider an inverse problem for the linearized Jordan–Moore–Gibson–Thompson equation, which is a third-order (in time) PDE that arises in nonlinear acoustic waves modeling high-intensity ultrasound. Both canonical recovery problems are investigated: (i) uniqueness and (ii) stability, by use of just one boundary measurement. Our approach relies on the dynamical decomposition of the Jordan–Moore–Gibson–Thompson equation given in [Math. Methods Appl. Sci. 35 (2012), 1896–1929].

Keywords: Inverse problem; third-order PDE equation; uniqueness; stability

About the article

Received: 2012-12-09

Published Online: 2013-11-02

Published in Print: 2013-12-01

Citation Information: Journal of Inverse and Ill-Posed Problems, Volume 21, Issue 6, Pages 825–869, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2012-0096.

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